A274071 --- a(n) is the least possible sum of a sequence of distinct terms consisting of exactly prime(i) multiples of prime(i) for i = 1 to n. Solutions for known and estimated terms. ---------------------------------------------------------------------------------- a1 = 6, max Prime = 2, # of terms = 2 Terms 2,4 1 2 2 4 Primes contained in the terms 2 ======= 2 2 4 2 ---------------------------------------------------------------------------------- a2 = 20, max Prime = 3, # of terms = 4 Terms 2,3,6,9 1 2 2 3 3 6 4 9 Primes contained in the terms 2 3 ========= 2 2 3 3 6 2 3 9 3 ---------------------------------------------------------------------------------- a3 = 87, max Prime = 5, # of terms = 7 Terms 3,5,9,10,15,20,25 1 3 2 5 3 9 4 10 5 15 6 20 7 25 Primes contained in the terms 2 3 5 =========== 3 3 5 5 9 3 10 2 5 15 3 5 20 2 5 25 5 ---------------------------------------------------------------------------------- a4 = 304, max Prime = 7, # of terms = 10 Terms 5,7,14,15,21,25,28,35,49,105 1 5 2 7 3 14 4 15 5 21 6 25 7 28 8 35 9 49 10 105 Primes contained in the terms 2 3 5 7 ============= 5 5 7 7 14 2 7 15 3 5 21 3 7 25 5 28 2 7 35 5 7 49 7 105 3 5 7 ---------------------------------------------------------------------------------- a4 = 304, max Prime = 7, # of terms = 10 Terms 5,7,14,15,21,25,35,49,63,70 1 5 2 7 3 14 4 15 5 21 6 25 7 35 8 49 9 63 10 70 Primes contained in the terms 2 3 5 7 ============= 5 5 7 7 14 2 7 15 3 5 21 3 7 25 5 35 5 7 49 7 63 3 7 70 2 5 7 ---------------------------------------------------------------------------------- a5 = 1559, max Prime = 11, # of terms = 15 Terms 5,7,11,22,33,35,49,55,77,99,121,154,231,275,385 1 5 2 7 3 11 4 22 5 33 6 35 7 49 8 55 9 77 10 99 11 121 12 154 13 231 14 275 15 385 Primes contained in the terms 2 3 5 7 11 ================ 5 5 7 7 11 11 22 2 11 33 3 11 35 5 7 49 7 55 5 11 77 7 11 99 3 11 121 11 154 2 7 11 231 3 7 11 275 5 11 385 5 7 11 ---------------------------------------------------------------------------------- a6 = 3582, max Prime = 13, # of terms = 26 Terms 7,11,13,26,33,35,39,49,55,65,77,91,117,119,121,143,169,187,209,221,247,253,286,299,325,385 1 7 2 11 3 13 4 26 5 33 6 35 7 39 8 49 9 55 10 65 11 77 12 91 13 117 14 119 15 121 16 143 17 169 18 187 19 209 20 221 21 247 22 253 23 286 24 299 25 325 26 385 Primes contained in the terms 2 3 5 7 11 13 =================== 7 7 11 11 13 13 26 2 13 33 3 11 35 5 7 39 3 13 49 7 55 5 11 65 5 13 77 7 11 91 7 13 117 3 13 119 7 (17) 121 11 143 11 13 169 13 187 11 (17) 209 11 (19) 221 13 (17) 247 13 (19) 253 11 (23) 286 2 11 13 299 13 (23) 325 5 13 385 5 7 11 ---------------------------------------------------------------------------------- a7 = 9218, max Prime = 17, # of terms = 38 Terms 7,11,13,17,49,51,55,65,77,85,91,119,121,133,143,153,169,187,209,221,247,253,289,299,319,323,341,374,377,391,403,425,442,481,493,527,595,663 1 7 2 11 3 13 4 17 5 49 6 51 7 55 8 65 9 77 10 85 11 91 12 119 13 121 14 133 15 143 16 153 17 169 18 187 19 209 20 221 21 247 22 253 23 289 24 299 25 319 26 323 27 341 28 374 29 377 30 391 31 403 32 425 33 442 34 481 35 493 36 527 37 595 38 663 Primes contained in the terms 2 3 5 7 11 13 17 ====================== 7 7 11 11 13 13 17 17 49 7 51 3 17 55 5 11 65 5 13 77 7 11 85 5 17 91 7 13 119 7 17 121 11 133 7 (19) 143 11 13 153 3 17 169 13 187 11 17 209 11 (19) 221 13 17 247 13 (19) 253 11 (23) 289 17 299 13 (23) 319 11 (29) 323 17 (19) 341 11 (31) 374 2 11 17 377 13 (29) 391 17 (23) 403 13 (31) 425 5 17 442 2 13 17 481 13 (37) 493 17 (29) 527 17 (31) 595 5 7 17 663 3 13 17 ---------------------------------------------------------------------------------- a8 = 18270, max Prime = 19, # of terms = 52 Terms 7,11,13,17,19,51,55,57,65,77,85,91,95,119,121,133,143,169,187,209,221,247,253,289,299,319,323,341,361,377,391,403,407,437,475,481,493,494,527,533,551,589,629,646,697,703,731,779,817,833,931,969 1 7 2 11 3 13 4 17 5 19 6 51 7 55 8 57 9 65 10 77 11 85 12 91 13 95 14 119 15 121 16 133 17 143 18 169 19 187 20 209 21 221 22 247 23 253 24 289 25 299 26 319 27 323 28 341 29 361 30 377 31 391 32 403 33 407 34 437 35 475 36 481 37 493 38 494 39 527 40 533 41 551 42 589 43 629 44 646 45 697 46 703 47 731 48 779 49 817 50 833 51 931 52 969 Primes contained in the terms 2 3 5 7 11 13 17 19 ========================= 7 7 11 11 13 13 17 17 19 19 51 3 17 55 5 11 57 3 19 65 5 13 77 7 11 85 5 17 91 7 13 95 5 19 119 7 17 121 11 133 7 19 143 11 13 169 13 187 11 17 209 11 19 221 13 17 247 13 19 253 11 (23) 289 17 299 13 (23) 319 11 (29) 323 17 19 341 11 (31) 361 19 377 13 (29) 391 17 (23) 403 13 (31) 407 11 (37) 437 19 (23) 475 5 19 481 13 (37) 493 17 (29) 494 2 13 19 527 17 (31) 533 13 (41) 551 19 (29) 589 19 (31) 629 17 (37) 646 2 17 19 697 17 (41) 703 19 (37) 731 17 (43) 779 19 (41) 817 19 (43) 833 7 17 931 7 19 969 3 17 19 ---------------------------------------------------------------------------------- a9 = 34873, max Prime = 23, # of terms = 69 Terms 11,13,17,19,23,69,77,85,91,95,115,119,121,133,143,161,169,187,209,221,247,253,289,299,319,323,341,361,377,391,403,407,437,451,475,481,493,527,529,533,551,559,575,589,611,629,667,697,703,713,731,779,782,799,817,851,874,893,901,931,943,989,1007,1081,1127,1173,1219,1311,1357 1 11 2 13 3 17 4 19 5 23 6 69 7 77 8 85 9 91 10 95 11 115 12 119 13 121 14 133 15 143 16 161 17 169 18 187 19 209 20 221 21 247 22 253 23 289 24 299 25 319 26 323 27 341 28 361 29 377 30 391 31 403 32 407 33 437 34 451 35 475 36 481 37 493 38 527 39 529 40 533 41 551 42 559 43 575 44 589 45 611 46 629 47 667 48 697 49 703 50 713 51 731 52 779 53 782 54 799 55 817 56 851 57 874 58 893 59 901 60 931 61 943 62 989 63 1007 64 1081 65 1127 66 1173 67 1219 68 1311 69 1357 Primes contained in the terms 2 3 5 7 11 13 17 19 23 ============================ 11 11 13 13 17 17 19 19 23 23 69 3 23 77 7 11 85 5 17 91 7 13 95 5 19 115 5 23 119 7 17 121 11 133 7 19 143 11 13 161 7 23 169 13 187 11 17 209 11 19 221 13 17 247 13 19 253 11 23 289 17 299 13 23 319 11 (29) 323 17 19 341 11 (31) 361 19 377 13 (29) 391 17 23 403 13 (31) 407 11 (37) 437 19 23 451 11 (41) 475 5 19 481 13 (37) 493 17 (29) 527 17 (31) 529 23 533 13 (41) 551 19 (29) 559 13 (43) 575 5 23 589 19 (31) 611 13 (47) 629 17 (37) 667 23 (29) 697 17 (41) 703 19 (37) 713 23 (31) 731 17 (43) 779 19 (41) 782 2 17 23 799 17 (47) 817 19 (43) 851 23 (37) 874 2 19 23 893 19 (47) 901 17 (53) 931 7 19 943 23 (41) 989 23 (43) 1007 19 (53) 1081 23 (47) 1127 7 23 1173 3 17 23 1219 23 (53) 1311 3 19 23 1357 23 (59) ---------------------------------------------------------------------------------- a10 = 70451, max Prime = 29, # of terms = 93 Terms 11,13,17,19,23,29,87,91,95,115,119,121,133,143,145,161,169,187,203,209,221,247,253,261,289,299,319,323,341,361,377,391,403,407,437,451,481,493,527,529,533,551,559,589,611,629,667,697,703,713,725,731,779,799,817,841,851,893,899,901,943,989,1003,1007,1037,1073,1081,1102,1121,1127,1139,1159,1189,1219,1247,1273,1334,1357,1363,1403,1421,1537,1541,1595,1633,1679,1711,1769,1943,2001,2059,2117,2291 1 11 2 13 3 17 4 19 5 23 6 29 7 87 8 91 9 95 10 115 11 119 12 121 13 133 14 143 15 145 16 161 17 169 18 187 19 203 20 209 21 221 22 247 23 253 24 261 25 289 26 299 27 319 28 323 29 341 30 361 31 377 32 391 33 403 34 407 35 437 36 451 37 481 38 493 39 527 40 529 41 533 42 551 43 559 44 589 45 611 46 629 47 667 48 697 49 703 50 713 51 725 52 731 53 779 54 799 55 817 56 841 57 851 58 893 59 899 60 901 61 943 62 989 63 1003 64 1007 65 1037 66 1073 67 1081 68 1102 69 1121 70 1127 71 1139 72 1159 73 1189 74 1219 75 1247 76 1273 77 1334 78 1357 79 1363 80 1403 81 1421 82 1537 83 1541 84 1595 85 1633 86 1679 87 1711 88 1769 89 1943 90 2001 91 2059 92 2117 93 2291 Primes contained in the terms 2 3 5 7 11 13 17 19 23 29 =============================== 11 11 13 13 17 17 19 19 23 23 29 29 87 3 29 91 7 13 95 5 19 115 5 23 119 7 17 121 11 133 7 19 143 11 13 145 5 29 161 7 23 169 13 187 11 17 203 7 29 209 11 19 221 13 17 247 13 19 253 11 23 261 3 29 289 17 299 13 23 319 11 29 323 17 19 341 11 (31) 361 19 377 13 29 391 17 23 403 13 (31) 407 11 (37) 437 19 23 451 11 (41) 481 13 (37) 493 17 29 527 17 (31) 529 23 533 13 (41) 551 19 29 559 13 (43) 589 19 (31) 611 13 (47) 629 17 (37) 667 23 29 697 17 (41) 703 19 (37) 713 23 (31) 725 5 29 731 17 (43) 779 19 (41) 799 17 (47) 817 19 (43) 841 29 851 23 (37) 893 19 (47) 899 29 (31) 901 17 (53) 943 23 (41) 989 23 (43) 1003 17 (59) 1007 19 (53) 1037 17 (61) 1073 29 (37) 1081 23 (47) 1102 2 19 29 1121 19 (59) 1127 7 23 1139 17 (67) 1159 19 (61) 1189 29 (41) 1219 23 (53) 1247 29 (43) 1273 19 (67) 1334 2 23 29 1357 23 (59) 1363 29 (47) 1403 23 (61) 1421 7 29 1537 29 (53) 1541 23 (67) 1595 5 11 29 1633 23 (71) 1679 23 (73) 1711 29 (59) 1769 29 (61) 1943 29 (67) 2001 3 23 29 2059 29 (71) 2117 29 (73) 2291 29 (79) ---------------------------------------------------------------------------------- a11 <= 118833, max Prime = 31, # of terms = 117 Terms 11,13,17,19,23,29,31,93,115,121,133,143,145,155,161,169,187,203,209,217,221,247,253,289,299,319,323,341,361,377,391,403,407,437,451,481,493,527,529,533,551,559,589,611,629,667,689,697,703,713,725,731,775,779,799,817,841,851,893,899,901,943,961,989,1003,1007,1037,1073,1081,1121,1139,1147,1159,1189,1207,1219,1247,1271,1273,1333,1349,1357,1363,1387,1403,1421,1426,1457,1519,1537,1541,1633,1643,1679,1711,1769,1798,1817,1829,1891,1943,2059,2077,2117,2139,2201,2233,2263,2291,2407,2449,2573,2581,2697,2759,2813,3007 1 11 2 13 3 17 4 19 5 23 6 29 7 31 8 93 9 115 10 121 11 133 12 143 13 145 14 155 15 161 16 169 17 187 18 203 19 209 20 217 21 221 22 247 23 253 24 289 25 299 26 319 27 323 28 341 29 361 30 377 31 391 32 403 33 407 34 437 35 451 36 481 37 493 38 527 39 529 40 533 41 551 42 559 43 589 44 611 45 629 46 667 47 689 48 697 49 703 50 713 51 725 52 731 53 775 54 779 55 799 56 817 57 841 58 851 59 893 60 899 61 901 62 943 63 961 64 989 65 1003 66 1007 67 1037 68 1073 69 1081 70 1121 71 1139 72 1147 73 1159 74 1189 75 1207 76 1219 77 1247 78 1271 79 1273 80 1333 81 1349 82 1357 83 1363 84 1387 85 1403 86 1421 87 1426 88 1457 89 1519 90 1537 91 1541 92 1633 93 1643 94 1679 95 1711 96 1769 97 1798 98 1817 99 1829 100 1891 101 1943 102 2059 103 2077 104 2117 105 2139 106 2201 107 2233 108 2263 109 2291 110 2407 111 2449 112 2573 113 2581 114 2697 115 2759 116 2813 117 3007 Primes contained in the terms 2 3 5 7 11 13 17 19 23 29 31 ================================== 11 11 13 13 17 17 19 19 23 23 29 29 31 31 93 3 31 115 5 23 121 11 133 7 19 143 11 13 145 5 29 155 5 31 161 7 23 169 13 187 11 17 203 7 29 209 11 19 217 7 31 221 13 17 247 13 19 253 11 23 289 17 299 13 23 319 11 29 323 17 19 341 11 31 361 19 377 13 29 391 17 23 403 13 31 407 11 (37) 437 19 23 451 11 (41) 481 13 (37) 493 17 29 527 17 31 529 23 533 13 (41) 551 19 29 559 13 (43) 589 19 31 611 13 (47) 629 17 (37) 667 23 29 689 13 (53) 697 17 (41) 703 19 (37) 713 23 31 725 5 29 731 17 (43) 775 5 31 779 19 (41) 799 17 (47) 817 19 (43) 841 29 851 23 (37) 893 19 (47) 899 29 31 901 17 (53) 943 23 (41) 961 31 989 23 (43) 1003 17 (59) 1007 19 (53) 1037 17 (61) 1073 29 (37) 1081 23 (47) 1121 19 (59) 1139 17 (67) 1147 31 (37) 1159 19 (61) 1189 29 (41) 1207 17 (71) 1219 23 (53) 1247 29 (43) 1271 31 (41) 1273 19 (67) 1333 31 (43) 1349 19 (71) 1357 23 (59) 1363 29 (47) 1387 19 (73) 1403 23 (61) 1421 7 29 1426 2 23 31 1457 31 (47) 1519 7 31 1537 29 (53) 1541 23 (67) 1633 23 (71) 1643 31 (53) 1679 23 (73) 1711 29 (59) 1769 29 (61) 1798 2 29 31 1817 23 (79) 1829 31 (59) 1891 31 (61) 1943 29 (67) 2059 29 (71) 2077 31 (67) 2117 29 (73) 2139 3 23 31 2201 31 (71) 2233 7 11 29 2263 31 (73) 2291 29 (79) 2407 29 (83) 2449 31 (79) 2573 31 (83) 2581 29 (89) 2697 3 29 31 2759 31 (89) 2813 29 (97) 3007 31 (97) ---------------------------------------------------------------------------------- a12 <= 202546, max Prime = 37, # of terms = 146 Terms 11,13,17,19,23,29,31,37,111,121,143,145,155,161,169,185,187,203,209,217,221,247,253,259,289,299,319,323,341,361,377,391,403,407,437,481,493,527,529,533,551,559,589,611,629,667,689,697,703,713,731,775,779,799,817,841,851,893,899,901,925,943,961,989,1003,1007,1037,1073,1081,1121,1139,1147,1159,1189,1207,1219,1247,1271,1273,1333,1349,1357,1363,1369,1387,1403,1457,1501,1517,1519,1537,1541,1591,1633,1643,1679,1711,1739,1769,1813,1817,1829,1891,1909,1943,1961,2047,2059,2077,2117,2146,2183,2201,2231,2257,2263,2291,2294,2407,2449,2479,2573,2581,2627,2701,2759,2813,2849,2923,2929,2987,3007,3071,3103,3131,3193,3219,3293,3317,3441,3589,3737,3811,3959,4033,4477 1 11 2 13 3 17 4 19 5 23 6 29 7 31 8 37 9 111 10 121 11 143 12 145 13 155 14 161 15 169 16 185 17 187 18 203 19 209 20 217 21 221 22 247 23 253 24 259 25 289 26 299 27 319 28 323 29 341 30 361 31 377 32 391 33 403 34 407 35 437 36 481 37 493 38 527 39 529 40 533 41 551 42 559 43 589 44 611 45 629 46 667 47 689 48 697 49 703 50 713 51 731 52 775 53 779 54 799 55 817 56 841 57 851 58 893 59 899 60 901 61 925 62 943 63 961 64 989 65 1003 66 1007 67 1037 68 1073 69 1081 70 1121 71 1139 72 1147 73 1159 74 1189 75 1207 76 1219 77 1247 78 1271 79 1273 80 1333 81 1349 82 1357 83 1363 84 1369 85 1387 86 1403 87 1457 88 1501 89 1517 90 1519 91 1537 92 1541 93 1591 94 1633 95 1643 96 1679 97 1711 98 1739 99 1769 100 1813 101 1817 102 1829 103 1891 104 1909 105 1943 106 1961 107 2047 108 2059 109 2077 110 2117 111 2146 112 2183 113 2201 114 2231 115 2257 116 2263 117 2291 118 2294 119 2407 120 2449 121 2479 122 2573 123 2581 124 2627 125 2701 126 2759 127 2813 128 2849 129 2923 130 2929 131 2987 132 3007 133 3071 134 3103 135 3131 136 3193 137 3219 138 3293 139 3317 140 3441 141 3589 142 3737 143 3811 144 3959 145 4033 146 4477 Primes contained in the terms 2 3 5 7 11 13 17 19 23 29 31 37 ===================================== 11 11 13 13 17 17 19 19 23 23 29 29 31 31 37 37 111 3 37 121 11 143 11 13 145 5 29 155 5 31 161 7 23 169 13 185 5 37 187 11 17 203 7 29 209 11 19 217 7 31 221 13 17 247 13 19 253 11 23 259 7 37 289 17 299 13 23 319 11 29 323 17 19 341 11 31 361 19 377 13 29 391 17 23 403 13 31 407 11 37 437 19 23 481 13 37 493 17 29 527 17 31 529 23 533 13 (41) 551 19 29 559 13 (43) 589 19 31 611 13 (47) 629 17 37 667 23 29 689 13 (53) 697 17 (41) 703 19 37 713 23 31 731 17 (43) 775 5 31 779 19 (41) 799 17 (47) 817 19 (43) 841 29 851 23 37 893 19 (47) 899 29 31 901 17 (53) 925 5 37 943 23 (41) 961 31 989 23 (43) 1003 17 (59) 1007 19 (53) 1037 17 (61) 1073 29 37 1081 23 (47) 1121 19 (59) 1139 17 (67) 1147 31 37 1159 19 (61) 1189 29 (41) 1207 17 (71) 1219 23 (53) 1247 29 (43) 1271 31 (41) 1273 19 (67) 1333 31 (43) 1349 19 (71) 1357 23 (59) 1363 29 (47) 1369 37 1387 19 (73) 1403 23 (61) 1457 31 (47) 1501 19 (79) 1517 37 (41) 1519 7 31 1537 29 (53) 1541 23 (67) 1591 37 (43) 1633 23 (71) 1643 31 (53) 1679 23 (73) 1711 29 (59) 1739 37 (47) 1769 29 (61) 1813 7 37 1817 23 (79) 1829 31 (59) 1891 31 (61) 1909 23 (83) 1943 29 (67) 1961 37 (53) 2047 23 (89) 2059 29 (71) 2077 31 (67) 2117 29 (73) 2146 2 29 37 2183 37 (59) 2201 31 (71) 2231 23 (97) 2257 37 (61) 2263 31 (73) 2291 29 (79) 2294 2 31 37 2407 29 (83) 2449 31 (79) 2479 37 (67) 2573 31 (83) 2581 29 (89) 2627 37 (71) 2701 37 (73) 2759 31 (89) 2813 29 (97) 2849 7 11 37 2923 37 (79) 2929 29 (101) 2987 29 (103) 3007 31 (97) 3071 37 (83) 3103 29 (107) 3131 31 (101) 3193 31 (103) 3219 3 29 37 3293 37 (89) 3317 31 (107) 3441 3 31 37 3589 37 (97) 3737 37 (101) 3811 37 (103) 3959 37 (107) 4033 37 (109) 4477 11 37 ---------------------------------------------------------------------------------- a13 <= 322763, max Prime = 41, # of terms = 175 Terms 13,17,19,23,29,31,37,41,143,155,169,185,187,203,205,209,217,221,247,253,259,287,289,299,319,323,341,361,377,391,403,407,437,451,481,493,527,529,533,551,559,589,629,667,697,703,713,731,779,799,817,841,851,893,899,901,925,943,961,989,1003,1007,1025,1037,1073,1081,1121,1139,1147,1159,1189,1207,1219,1247,1271,1273,1333,1349,1357,1363,1369,1387,1403,1457,1501,1517,1537,1541,1591,1633,1643,1679,1681,1711,1739,1763,1769,1813,1817,1829,1891,1909,1927,1943,1961,2009,2047,2059,2077,2117,2173,2183,2201,2231,2257,2263,2291,2323,2407,2419,2449,2479,2501,2542,2573,2581,2627,2701,2747,2759,2813,2911,2923,2929,2987,2993,3007,3034,3071,3103,3131,3161,3193,3239,3277,3293,3317,3379,3403,3503,3567,3589,3649,3731,3737,3811,3813,3959,3977,4033,4141,4181,4223,4387,4469,4477,4551,4633,4699,4847,4961,5207,5291,5371,5617 1 13 2 17 3 19 4 23 5 29 6 31 7 37 8 41 9 143 10 155 11 169 12 185 13 187 14 203 15 205 16 209 17 217 18 221 19 247 20 253 21 259 22 287 23 289 24 299 25 319 26 323 27 341 28 361 29 377 30 391 31 403 32 407 33 437 34 451 35 481 36 493 37 527 38 529 39 533 40 551 41 559 42 589 43 629 44 667 45 697 46 703 47 713 48 731 49 779 50 799 51 817 52 841 53 851 54 893 55 899 56 901 57 925 58 943 59 961 60 989 61 1003 62 1007 63 1025 64 1037 65 1073 66 1081 67 1121 68 1139 69 1147 70 1159 71 1189 72 1207 73 1219 74 1247 75 1271 76 1273 77 1333 78 1349 79 1357 80 1363 81 1369 82 1387 83 1403 84 1457 85 1501 86 1517 87 1537 88 1541 89 1591 90 1633 91 1643 92 1679 93 1681 94 1711 95 1739 96 1763 97 1769 98 1813 99 1817 100 1829 101 1891 102 1909 103 1927 104 1943 105 1961 106 2009 107 2047 108 2059 109 2077 110 2117 111 2173 112 2183 113 2201 114 2231 115 2257 116 2263 117 2291 118 2323 119 2407 120 2419 121 2449 122 2479 123 2501 124 2542 125 2573 126 2581 127 2627 128 2701 129 2747 130 2759 131 2813 132 2911 133 2923 134 2929 135 2987 136 2993 137 3007 138 3034 139 3071 140 3103 141 3131 142 3161 143 3193 144 3239 145 3277 146 3293 147 3317 148 3379 149 3403 150 3503 151 3567 152 3589 153 3649 154 3731 155 3737 156 3811 157 3813 158 3959 159 3977 160 4033 161 4141 162 4181 163 4223 164 4387 165 4469 166 4477 167 4551 168 4633 169 4699 170 4847 171 4961 172 5207 173 5291 174 5371 175 5617 Primes contained in the terms 2 3 5 7 11 13 17 19 23 29 31 37 41 ======================================== 13 13 17 17 19 19 23 23 29 29 31 31 37 37 41 41 143 11 13 155 5 31 169 13 185 5 37 187 11 17 203 7 29 205 5 41 209 11 19 217 7 31 221 13 17 247 13 19 253 11 23 259 7 37 287 7 41 289 17 299 13 23 319 11 29 323 17 19 341 11 31 361 19 377 13 29 391 17 23 403 13 31 407 11 37 437 19 23 451 11 41 481 13 37 493 17 29 527 17 31 529 23 533 13 41 551 19 29 559 13 (43) 589 19 31 629 17 37 667 23 29 697 17 41 703 19 37 713 23 31 731 17 (43) 779 19 41 799 17 (47) 817 19 (43) 841 29 851 23 37 893 19 (47) 899 29 31 901 17 (53) 925 5 37 943 23 41 961 31 989 23 (43) 1003 17 (59) 1007 19 (53) 1025 5 41 1037 17 (61) 1073 29 37 1081 23 (47) 1121 19 (59) 1139 17 (67) 1147 31 37 1159 19 (61) 1189 29 41 1207 17 (71) 1219 23 (53) 1247 29 (43) 1271 31 41 1273 19 (67) 1333 31 (43) 1349 19 (71) 1357 23 (59) 1363 29 (47) 1369 37 1387 19 (73) 1403 23 (61) 1457 31 (47) 1501 19 (79) 1517 37 41 1537 29 (53) 1541 23 (67) 1591 37 (43) 1633 23 (71) 1643 31 (53) 1679 23 (73) 1681 41 1711 29 (59) 1739 37 (47) 1763 41 (43) 1769 29 (61) 1813 7 37 1817 23 (79) 1829 31 (59) 1891 31 (61) 1909 23 (83) 1927 41 (47) 1943 29 (67) 1961 37 (53) 2009 7 41 2047 23 (89) 2059 29 (71) 2077 31 (67) 2117 29 (73) 2173 41 (53) 2183 37 (59) 2201 31 (71) 2231 23 (97) 2257 37 (61) 2263 31 (73) 2291 29 (79) 2323 23 (101) 2407 29 (83) 2419 41 (59) 2449 31 (79) 2479 37 (67) 2501 41 (61) 2542 2 31 41 2573 31 (83) 2581 29 (89) 2627 37 (71) 2701 37 (73) 2747 41 (67) 2759 31 (89) 2813 29 (97) 2911 41 (71) 2923 37 (79) 2929 29 (101) 2987 29 (103) 2993 41 (73) 3007 31 (97) 3034 2 37 41 3071 37 (83) 3103 29 (107) 3131 31 (101) 3161 29 (109) 3193 31 (103) 3239 41 (79) 3277 29 (113) 3293 37 (89) 3317 31 (107) 3379 31 (109) 3403 41 (83) 3503 31 (113) 3567 3 29 41 3589 37 (97) 3649 41 (89) 3731 7 13 41 3737 37 (101) 3811 37 (103) 3813 3 31 41 3959 37 (107) 3977 41 (97) 4033 37 (109) 4141 41 (101) 4181 37 (113) 4223 41 (103) 4387 41 (107) 4469 41 (109) 4477 11 37 4551 3 37 41 4633 41 (113) 4699 37 (127) 4847 37 (131) 4961 11 41 5207 41 (127) 5291 11 13 37 5371 41 (131) 5617 41 (137) ---------------------------------------------------------------------------------- a14 <= 470583, max Prime = 43, # of terms = 211 Terms 13,17,19,23,29,31,37,41,43,169,185,187,205,209,215,217,221,247,253,259,287,289,299,301,319,323,341,361,377,391,403,407,437,451,473,481,493,527,529,533,551,559,589,611,629,667,689,697,703,713,731,779,799,817,841,851,893,899,901,943,961,989,1003,1007,1025,1037,1073,1075,1081,1121,1139,1147,1159,1189,1207,1219,1247,1271,1273,1333,1349,1357,1363,1369,1387,1403,1457,1501,1517,1537,1541,1591,1633,1643,1679,1681,1711,1739,1763,1769,1813,1817,1829,1849,1891,1909,1927,1943,1961,2009,2021,2047,2059,2077,2107,2117,2173,2183,2201,2231,2257,2263,2279,2291,2323,2407,2419,2449,2479,2501,2537,2573,2581,2623,2627,2701,2747,2759,2813,2881,2911,2923,2929,2987,2993,3007,3053,3071,3103,3131,3139,3161,3182,3193,3239,3277,3293,3317,3379,3397,3403,3503,3526,3569,3589,3649,3683,3737,3799,3811,3827,3937,3959,3977,4033,4061,4141,4171,4181,4223,4247,4343,4387,4429,4469,4551,4601,4633,4687,4699,4773,4847,4859,4961,5069,5143,5203,5207,5289,5371,5461,5617,5633,5699,5891,5977,6109,6149,6191,6407,6493 1 13 2 17 3 19 4 23 5 29 6 31 7 37 8 41 9 43 10 169 11 185 12 187 13 205 14 209 15 215 16 217 17 221 18 247 19 253 20 259 21 287 22 289 23 299 24 301 25 319 26 323 27 341 28 361 29 377 30 391 31 403 32 407 33 437 34 451 35 473 36 481 37 493 38 527 39 529 40 533 41 551 42 559 43 589 44 611 45 629 46 667 47 689 48 697 49 703 50 713 51 731 52 779 53 799 54 817 55 841 56 851 57 893 58 899 59 901 60 943 61 961 62 989 63 1003 64 1007 65 1025 66 1037 67 1073 68 1075 69 1081 70 1121 71 1139 72 1147 73 1159 74 1189 75 1207 76 1219 77 1247 78 1271 79 1273 80 1333 81 1349 82 1357 83 1363 84 1369 85 1387 86 1403 87 1457 88 1501 89 1517 90 1537 91 1541 92 1591 93 1633 94 1643 95 1679 96 1681 97 1711 98 1739 99 1763 100 1769 101 1813 102 1817 103 1829 104 1849 105 1891 106 1909 107 1927 108 1943 109 1961 110 2009 111 2021 112 2047 113 2059 114 2077 115 2107 116 2117 117 2173 118 2183 119 2201 120 2231 121 2257 122 2263 123 2279 124 2291 125 2323 126 2407 127 2419 128 2449 129 2479 130 2501 131 2537 132 2573 133 2581 134 2623 135 2627 136 2701 137 2747 138 2759 139 2813 140 2881 141 2911 142 2923 143 2929 144 2987 145 2993 146 3007 147 3053 148 3071 149 3103 150 3131 151 3139 152 3161 153 3182 154 3193 155 3239 156 3277 157 3293 158 3317 159 3379 160 3397 161 3403 162 3503 163 3526 164 3569 165 3589 166 3649 167 3683 168 3737 169 3799 170 3811 171 3827 172 3937 173 3959 174 3977 175 4033 176 4061 177 4141 178 4171 179 4181 180 4223 181 4247 182 4343 183 4387 184 4429 185 4469 186 4551 187 4601 188 4633 189 4687 190 4699 191 4773 192 4847 193 4859 194 4961 195 5069 196 5143 197 5203 198 5207 199 5289 200 5371 201 5461 202 5617 203 5633 204 5699 205 5891 206 5977 207 6109 208 6149 209 6191 210 6407 211 6493 Primes contained in the terms 2 3 5 7 11 13 17 19 23 29 31 37 41 43 =========================================== 13 13 17 17 19 19 23 23 29 29 31 31 37 37 41 41 43 43 169 13 185 5 37 187 11 17 205 5 41 209 11 19 215 5 43 217 7 31 221 13 17 247 13 19 253 11 23 259 7 37 287 7 41 289 17 299 13 23 301 7 43 319 11 29 323 17 19 341 11 31 361 19 377 13 29 391 17 23 403 13 31 407 11 37 437 19 23 451 11 41 473 11 43 481 13 37 493 17 29 527 17 31 529 23 533 13 41 551 19 29 559 13 43 589 19 31 611 13 (47) 629 17 37 667 23 29 689 13 (53) 697 17 41 703 19 37 713 23 31 731 17 43 779 19 41 799 17 (47) 817 19 43 841 29 851 23 37 893 19 (47) 899 29 31 901 17 (53) 943 23 41 961 31 989 23 43 1003 17 (59) 1007 19 (53) 1025 5 41 1037 17 (61) 1073 29 37 1075 5 43 1081 23 (47) 1121 19 (59) 1139 17 (67) 1147 31 37 1159 19 (61) 1189 29 41 1207 17 (71) 1219 23 (53) 1247 29 43 1271 31 41 1273 19 (67) 1333 31 43 1349 19 (71) 1357 23 (59) 1363 29 (47) 1369 37 1387 19 (73) 1403 23 (61) 1457 31 (47) 1501 19 (79) 1517 37 41 1537 29 (53) 1541 23 (67) 1591 37 43 1633 23 (71) 1643 31 (53) 1679 23 (73) 1681 41 1711 29 (59) 1739 37 (47) 1763 41 43 1769 29 (61) 1813 7 37 1817 23 (79) 1829 31 (59) 1849 43 1891 31 (61) 1909 23 (83) 1927 41 (47) 1943 29 (67) 1961 37 (53) 2009 7 41 2021 43 (47) 2047 23 (89) 2059 29 (71) 2077 31 (67) 2107 7 43 2117 29 (73) 2173 41 (53) 2183 37 (59) 2201 31 (71) 2231 23 (97) 2257 37 (61) 2263 31 (73) 2279 43 (53) 2291 29 (79) 2323 23 (101) 2407 29 (83) 2419 41 (59) 2449 31 (79) 2479 37 (67) 2501 41 (61) 2537 43 (59) 2573 31 (83) 2581 29 (89) 2623 43 (61) 2627 37 (71) 2701 37 (73) 2747 41 (67) 2759 31 (89) 2813 29 (97) 2881 43 (67) 2911 41 (71) 2923 37 (79) 2929 29 (101) 2987 29 (103) 2993 41 (73) 3007 31 (97) 3053 43 (71) 3071 37 (83) 3103 29 (107) 3131 31 (101) 3139 43 (73) 3161 29 (109) 3182 2 37 43 3193 31 (103) 3239 41 (79) 3277 29 (113) 3293 37 (89) 3317 31 (107) 3379 31 (109) 3397 43 (79) 3403 41 (83) 3503 31 (113) 3526 2 41 43 3569 43 (83) 3589 37 (97) 3649 41 (89) 3683 29 (127) 3737 37 (101) 3799 29 (131) 3811 37 (103) 3827 43 (89) 3937 31 (127) 3959 37 (107) 3977 41 (97) 4033 37 (109) 4061 31 (131) 4141 41 (101) 4171 43 (97) 4181 37 (113) 4223 41 (103) 4247 31 (137) 4343 43 (101) 4387 41 (107) 4429 43 (103) 4469 41 (109) 4551 3 37 41 4601 43 (107) 4633 41 (113) 4687 43 (109) 4699 37 (127) 4773 3 37 43 4847 37 (131) 4859 43 (113) 4961 11 41 5069 37 (137) 5143 37 (139) 5203 11 43 5207 41 (127) 5289 3 41 43 5371 41 (131) 5461 43 (127) 5617 41 (137) 5633 43 (131) 5699 41 (139) 5891 43 (137) 5977 43 (139) 6109 41 (149) 6149 11 13 43 6191 41 (151) 6407 43 (149) 6493 43 (151) ---------------------------------------------------------------------------------- a15 <= 668392, max Prime = 47, # of terms = 248 Terms 13,17,19,23,29,31,37,41,43,47,169,205,215,221,235,247,253,259,287,289,299,301,319,323,329,341,361,377,391,403,407,437,451,473,481,493,517,527,529,533,551,559,589,611,629,667,697,703,713,731,779,799,817,841,851,893,899,901,943,961,989,1003,1007,1037,1073,1075,1081,1121,1139,1147,1159,1175,1189,1207,1219,1241,1247,1271,1273,1333,1349,1357,1363,1369,1387,1403,1457,1501,1517,1537,1541,1577,1591,1633,1643,1679,1681,1711,1739,1763,1769,1817,1829,1849,1891,1909,1927,1943,1961,2009,2021,2047,2059,2077,2107,2117,2173,2183,2201,2209,2231,2257,2263,2279,2291,2303,2323,2407,2419,2449,2479,2491,2501,2537,2573,2581,2623,2627,2701,2747,2759,2773,2813,2867,2881,2911,2923,2929,2987,2993,3007,3053,3071,3103,3131,3139,3149,3161,3193,3239,3277,3293,3317,3337,3379,3397,3403,3431,3503,3569,3589,3649,3683,3713,3737,3799,3811,3827,3854,3901,3937,3959,3977,4033,4042,4061,4141,4171,4181,4183,4223,4247,4309,4343,4387,4429,4469,4477,4559,4601,4633,4687,4699,4747,4841,4847,4859,4961,5029,5069,5123,5143,5203,5207,5217,5311,5371,5461,5513,5587,5617,5633,5687,5699,5781,5809,5891,5969,5977,6063,6109,6157,6191,6407,6437,6439,6493,6533,6683,6751,7003,7009,7097,7267,7379,7661,7849,7943 1 13 2 17 3 19 4 23 5 29 6 31 7 37 8 41 9 43 10 47 11 169 12 205 13 215 14 221 15 235 16 247 17 253 18 259 19 287 20 289 21 299 22 301 23 319 24 323 25 329 26 341 27 361 28 377 29 391 30 403 31 407 32 437 33 451 34 473 35 481 36 493 37 517 38 527 39 529 40 533 41 551 42 559 43 589 44 611 45 629 46 667 47 697 48 703 49 713 50 731 51 779 52 799 53 817 54 841 55 851 56 893 57 899 58 901 59 943 60 961 61 989 62 1003 63 1007 64 1037 65 1073 66 1075 67 1081 68 1121 69 1139 70 1147 71 1159 72 1175 73 1189 74 1207 75 1219 76 1241 77 1247 78 1271 79 1273 80 1333 81 1349 82 1357 83 1363 84 1369 85 1387 86 1403 87 1457 88 1501 89 1517 90 1537 91 1541 92 1577 93 1591 94 1633 95 1643 96 1679 97 1681 98 1711 99 1739 100 1763 101 1769 102 1817 103 1829 104 1849 105 1891 106 1909 107 1927 108 1943 109 1961 110 2009 111 2021 112 2047 113 2059 114 2077 115 2107 116 2117 117 2173 118 2183 119 2201 120 2209 121 2231 122 2257 123 2263 124 2279 125 2291 126 2303 127 2323 128 2407 129 2419 130 2449 131 2479 132 2491 133 2501 134 2537 135 2573 136 2581 137 2623 138 2627 139 2701 140 2747 141 2759 142 2773 143 2813 144 2867 145 2881 146 2911 147 2923 148 2929 149 2987 150 2993 151 3007 152 3053 153 3071 154 3103 155 3131 156 3139 157 3149 158 3161 159 3193 160 3239 161 3277 162 3293 163 3317 164 3337 165 3379 166 3397 167 3403 168 3431 169 3503 170 3569 171 3589 172 3649 173 3683 174 3713 175 3737 176 3799 177 3811 178 3827 179 3854 180 3901 181 3937 182 3959 183 3977 184 4033 185 4042 186 4061 187 4141 188 4171 189 4181 190 4183 191 4223 192 4247 193 4309 194 4343 195 4387 196 4429 197 4469 198 4477 199 4559 200 4601 201 4633 202 4687 203 4699 204 4747 205 4841 206 4847 207 4859 208 4961 209 5029 210 5069 211 5123 212 5143 213 5203 214 5207 215 5217 216 5311 217 5371 218 5461 219 5513 220 5587 221 5617 222 5633 223 5687 224 5699 225 5781 226 5809 227 5891 228 5969 229 5977 230 6063 231 6109 232 6157 233 6191 234 6407 235 6437 236 6439 237 6493 238 6533 239 6683 240 6751 241 7003 242 7009 243 7097 244 7267 245 7379 246 7661 247 7849 248 7943 Primes contained in the terms 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 ============================================== 13 13 17 17 19 19 23 23 29 29 31 31 37 37 41 41 43 43 47 47 169 13 205 5 41 215 5 43 221 13 17 235 5 47 247 13 19 253 11 23 259 7 37 287 7 41 289 17 299 13 23 301 7 43 319 11 29 323 17 19 329 7 47 341 11 31 361 19 377 13 29 391 17 23 403 13 31 407 11 37 437 19 23 451 11 41 473 11 43 481 13 37 493 17 29 517 11 47 527 17 31 529 23 533 13 41 551 19 29 559 13 43 589 19 31 611 13 47 629 17 37 667 23 29 697 17 41 703 19 37 713 23 31 731 17 43 779 19 41 799 17 47 817 19 43 841 29 851 23 37 893 19 47 899 29 31 901 17 (53) 943 23 41 961 31 989 23 43 1003 17 (59) 1007 19 (53) 1037 17 (61) 1073 29 37 1075 5 43 1081 23 47 1121 19 (59) 1139 17 (67) 1147 31 37 1159 19 (61) 1175 5 47 1189 29 41 1207 17 (71) 1219 23 (53) 1241 17 (73) 1247 29 43 1271 31 41 1273 19 (67) 1333 31 43 1349 19 (71) 1357 23 (59) 1363 29 47 1369 37 1387 19 (73) 1403 23 (61) 1457 31 47 1501 19 (79) 1517 37 41 1537 29 (53) 1541 23 (67) 1577 19 (83) 1591 37 43 1633 23 (71) 1643 31 (53) 1679 23 (73) 1681 41 1711 29 (59) 1739 37 47 1763 41 43 1769 29 (61) 1817 23 (79) 1829 31 (59) 1849 43 1891 31 (61) 1909 23 (83) 1927 41 47 1943 29 (67) 1961 37 (53) 2009 7 41 2021 43 47 2047 23 (89) 2059 29 (71) 2077 31 (67) 2107 7 43 2117 29 (73) 2173 41 (53) 2183 37 (59) 2201 31 (71) 2209 47 2231 23 (97) 2257 37 (61) 2263 31 (73) 2279 43 (53) 2291 29 (79) 2303 7 47 2323 23 (101) 2407 29 (83) 2419 41 (59) 2449 31 (79) 2479 37 (67) 2491 47 (53) 2501 41 (61) 2537 43 (59) 2573 31 (83) 2581 29 (89) 2623 43 (61) 2627 37 (71) 2701 37 (73) 2747 41 (67) 2759 31 (89) 2773 47 (59) 2813 29 (97) 2867 47 (61) 2881 43 (67) 2911 41 (71) 2923 37 (79) 2929 29 (101) 2987 29 (103) 2993 41 (73) 3007 31 (97) 3053 43 (71) 3071 37 (83) 3103 29 (107) 3131 31 (101) 3139 43 (73) 3149 47 (67) 3161 29 (109) 3193 31 (103) 3239 41 (79) 3277 29 (113) 3293 37 (89) 3317 31 (107) 3337 47 (71) 3379 31 (109) 3397 43 (79) 3403 41 (83) 3431 47 (73) 3503 31 (113) 3569 43 (83) 3589 37 (97) 3649 41 (89) 3683 29 (127) 3713 47 (79) 3737 37 (101) 3799 29 (131) 3811 37 (103) 3827 43 (89) 3854 2 41 47 3901 47 (83) 3937 31 (127) 3959 37 (107) 3977 41 (97) 4033 37 (109) 4042 2 43 47 4061 31 (131) 4141 41 (101) 4171 43 (97) 4181 37 (113) 4183 47 (89) 4223 41 (103) 4247 31 (137) 4309 31 (139) 4343 43 (101) 4387 41 (107) 4429 43 (103) 4469 41 (109) 4477 11 37 4559 47 (97) 4601 43 (107) 4633 41 (113) 4687 43 (109) 4699 37 (127) 4747 47 (101) 4841 47 (103) 4847 37 (131) 4859 43 (113) 4961 11 41 5029 47 (107) 5069 37 (137) 5123 47 (109) 5143 37 (139) 5203 11 43 5207 41 (127) 5217 3 37 47 5311 47 (113) 5371 41 (131) 5461 43 (127) 5513 37 (149) 5587 37 (151) 5617 41 (137) 5633 43 (131) 5687 11 47 5699 41 (139) 5781 3 41 47 5809 37 (157) 5891 43 (137) 5969 47 (127) 5977 43 (139) 6063 3 43 47 6109 41 (149) 6157 47 (131) 6191 41 (151) 6407 43 (149) 6437 41 (157) 6439 47 (137) 6493 43 (151) 6533 47 (139) 6683 41 (163) 6751 43 (157) 7003 47 (149) 7009 43 (163) 7097 47 (151) 7267 13 43 7379 47 (157) 7661 47 (163) 7849 47 (167) 7943 13 47 ---------------------------------------------------------------------------------- a16 <= 956378, max Prime = 53, # of terms = 290 Terms 17,19,23,29,31,37,41,43,47,53,215,221,235,247,259,265,287,289,299,301,319,323,329,341,361,371,377,391,403,407,437,451,473,481,493,517,527,529,533,551,559,583,589,611,629,667,689,697,703,713,731,779,799,817,841,851,893,899,901,943,961,989,1003,1007,1037,1073,1081,1121,1139,1147,1159,1175,1189,1207,1219,1241,1247,1271,1273,1325,1333,1349,1357,1363,1369,1387,1403,1457,1501,1517,1537,1541,1577,1591,1633,1643,1679,1681,1711,1739,1763,1769,1817,1829,1849,1891,1909,1927,1943,1961,2021,2047,2059,2077,2117,2173,2183,2201,2209,2231,2257,2263,2279,2291,2303,2323,2369,2407,2419,2449,2479,2491,2501,2537,2573,2581,2597,2623,2627,2701,2747,2759,2773,2809,2813,2867,2881,2911,2923,2929,2987,2993,3007,3053,3071,3103,3127,3131,3139,3149,3161,3193,3233,3239,3277,3293,3317,3337,3379,3397,3403,3431,3503,3551,3569,3589,3649,3683,3713,3737,3763,3799,3811,3827,3869,3901,3937,3959,3977,4033,4061,4141,4171,4181,4183,4187,4223,4247,4309,4343,4387,4399,4429,4469,4558,4559,4601,4633,4687,4699,4717,4747,4841,4847,4859,4961,4982,5029,5069,5123,5141,5143,5203,5207,5311,5353,5371,5459,5461,5513,5587,5617,5633,5671,5687,5699,5777,5809,5891,5969,5977,5989,6031,6109,6157,6179,6191,6407,6413,6437,6439,6493,6519,6533,6683,6731,6751,6837,6847,6943,7003,7009,7093,7097,7181,7261,7267,7339,7367,7379,7439,7473,7661,7849,7897,7943,8003,8131,8321,8413,8507,8639,8851,8957,9169,9487,9593,10123,10229,10441 1 17 2 19 3 23 4 29 5 31 6 37 7 41 8 43 9 47 10 53 11 215 12 221 13 235 14 247 15 259 16 265 17 287 18 289 19 299 20 301 21 319 22 323 23 329 24 341 25 361 26 371 27 377 28 391 29 403 30 407 31 437 32 451 33 473 34 481 35 493 36 517 37 527 38 529 39 533 40 551 41 559 42 583 43 589 44 611 45 629 46 667 47 689 48 697 49 703 50 713 51 731 52 779 53 799 54 817 55 841 56 851 57 893 58 899 59 901 60 943 61 961 62 989 63 1003 64 1007 65 1037 66 1073 67 1081 68 1121 69 1139 70 1147 71 1159 72 1175 73 1189 74 1207 75 1219 76 1241 77 1247 78 1271 79 1273 80 1325 81 1333 82 1349 83 1357 84 1363 85 1369 86 1387 87 1403 88 1457 89 1501 90 1517 91 1537 92 1541 93 1577 94 1591 95 1633 96 1643 97 1679 98 1681 99 1711 100 1739 101 1763 102 1769 103 1817 104 1829 105 1849 106 1891 107 1909 108 1927 109 1943 110 1961 111 2021 112 2047 113 2059 114 2077 115 2117 116 2173 117 2183 118 2201 119 2209 120 2231 121 2257 122 2263 123 2279 124 2291 125 2303 126 2323 127 2369 128 2407 129 2419 130 2449 131 2479 132 2491 133 2501 134 2537 135 2573 136 2581 137 2597 138 2623 139 2627 140 2701 141 2747 142 2759 143 2773 144 2809 145 2813 146 2867 147 2881 148 2911 149 2923 150 2929 151 2987 152 2993 153 3007 154 3053 155 3071 156 3103 157 3127 158 3131 159 3139 160 3149 161 3161 162 3193 163 3233 164 3239 165 3277 166 3293 167 3317 168 3337 169 3379 170 3397 171 3403 172 3431 173 3503 174 3551 175 3569 176 3589 177 3649 178 3683 179 3713 180 3737 181 3763 182 3799 183 3811 184 3827 185 3869 186 3901 187 3937 188 3959 189 3977 190 4033 191 4061 192 4141 193 4171 194 4181 195 4183 196 4187 197 4223 198 4247 199 4309 200 4343 201 4387 202 4399 203 4429 204 4469 205 4558 206 4559 207 4601 208 4633 209 4687 210 4699 211 4717 212 4747 213 4841 214 4847 215 4859 216 4961 217 4982 218 5029 219 5069 220 5123 221 5141 222 5143 223 5203 224 5207 225 5311 226 5353 227 5371 228 5459 229 5461 230 5513 231 5587 232 5617 233 5633 234 5671 235 5687 236 5699 237 5777 238 5809 239 5891 240 5969 241 5977 242 5989 243 6031 244 6109 245 6157 246 6179 247 6191 248 6407 249 6413 250 6437 251 6439 252 6493 253 6519 254 6533 255 6683 256 6731 257 6751 258 6837 259 6847 260 6943 261 7003 262 7009 263 7093 264 7097 265 7181 266 7261 267 7267 268 7339 269 7367 270 7379 271 7439 272 7473 273 7661 274 7849 275 7897 276 7943 277 8003 278 8131 279 8321 280 8413 281 8507 282 8639 283 8851 284 8957 285 9169 286 9487 287 9593 288 10123 289 10229 290 10441 Primes contained in the terms 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 ================================================= 17 17 19 19 23 23 29 29 31 31 37 37 41 41 43 43 47 47 53 53 215 5 43 221 13 17 235 5 47 247 13 19 259 7 37 265 5 53 287 7 41 289 17 299 13 23 301 7 43 319 11 29 323 17 19 329 7 47 341 11 31 361 19 371 7 53 377 13 29 391 17 23 403 13 31 407 11 37 437 19 23 451 11 41 473 11 43 481 13 37 493 17 29 517 11 47 527 17 31 529 23 533 13 41 551 19 29 559 13 43 583 11 53 589 19 31 611 13 47 629 17 37 667 23 29 689 13 53 697 17 41 703 19 37 713 23 31 731 17 43 779 19 41 799 17 47 817 19 43 841 29 851 23 37 893 19 47 899 29 31 901 17 53 943 23 41 961 31 989 23 43 1003 17 (59) 1007 19 53 1037 17 (61) 1073 29 37 1081 23 47 1121 19 (59) 1139 17 (67) 1147 31 37 1159 19 (61) 1175 5 47 1189 29 41 1207 17 (71) 1219 23 53 1241 17 (73) 1247 29 43 1271 31 41 1273 19 (67) 1325 5 53 1333 31 43 1349 19 (71) 1357 23 (59) 1363 29 47 1369 37 1387 19 (73) 1403 23 (61) 1457 31 47 1501 19 (79) 1517 37 41 1537 29 53 1541 23 (67) 1577 19 (83) 1591 37 43 1633 23 (71) 1643 31 53 1679 23 (73) 1681 41 1711 29 (59) 1739 37 47 1763 41 43 1769 29 (61) 1817 23 (79) 1829 31 (59) 1849 43 1891 31 (61) 1909 23 (83) 1927 41 47 1943 29 (67) 1961 37 53 2021 43 47 2047 23 (89) 2059 29 (71) 2077 31 (67) 2117 29 (73) 2173 41 53 2183 37 (59) 2201 31 (71) 2209 47 2231 23 (97) 2257 37 (61) 2263 31 (73) 2279 43 53 2291 29 (79) 2303 7 47 2323 23 (101) 2369 23 (103) 2407 29 (83) 2419 41 (59) 2449 31 (79) 2479 37 (67) 2491 47 53 2501 41 (61) 2537 43 (59) 2573 31 (83) 2581 29 (89) 2597 7 53 2623 43 (61) 2627 37 (71) 2701 37 (73) 2747 41 (67) 2759 31 (89) 2773 47 (59) 2809 53 2813 29 (97) 2867 47 (61) 2881 43 (67) 2911 41 (71) 2923 37 (79) 2929 29 (101) 2987 29 (103) 2993 41 (73) 3007 31 (97) 3053 43 (71) 3071 37 (83) 3103 29 (107) 3127 53 (59) 3131 31 (101) 3139 43 (73) 3149 47 (67) 3161 29 (109) 3193 31 (103) 3233 53 (61) 3239 41 (79) 3277 29 (113) 3293 37 (89) 3317 31 (107) 3337 47 (71) 3379 31 (109) 3397 43 (79) 3403 41 (83) 3431 47 (73) 3503 31 (113) 3551 53 (67) 3569 43 (83) 3589 37 (97) 3649 41 (89) 3683 29 (127) 3713 47 (79) 3737 37 (101) 3763 53 (71) 3799 29 (131) 3811 37 (103) 3827 43 (89) 3869 53 (73) 3901 47 (83) 3937 31 (127) 3959 37 (107) 3977 41 (97) 4033 37 (109) 4061 31 (131) 4141 41 (101) 4171 43 (97) 4181 37 (113) 4183 47 (89) 4187 53 (79) 4223 41 (103) 4247 31 (137) 4309 31 (139) 4343 43 (101) 4387 41 (107) 4399 53 (83) 4429 43 (103) 4469 41 (109) 4558 2 43 53 4559 47 (97) 4601 43 (107) 4633 41 (113) 4687 43 (109) 4699 37 (127) 4717 53 (89) 4747 47 (101) 4841 47 (103) 4847 37 (131) 4859 43 (113) 4961 11 41 4982 2 47 53 5029 47 (107) 5069 37 (137) 5123 47 (109) 5141 53 (97) 5143 37 (139) 5203 11 43 5207 41 (127) 5311 47 (113) 5353 53 (101) 5371 41 (131) 5459 53 (103) 5461 43 (127) 5513 37 (149) 5587 37 (151) 5617 41 (137) 5633 43 (131) 5671 53 (107) 5687 11 47 5699 41 (139) 5777 53 (109) 5809 37 (157) 5891 43 (137) 5969 47 (127) 5977 43 (139) 5989 53 (113) 6031 37 (163) 6109 41 (149) 6157 47 (131) 6179 37 (167) 6191 41 (151) 6407 43 (149) 6413 11 53 6437 41 (157) 6439 47 (137) 6493 43 (151) 6519 3 41 53 6533 47 (139) 6683 41 (163) 6731 53 (127) 6751 43 (157) 6837 3 43 53 6847 41 (167) 6943 53 (131) 7003 47 (149) 7009 43 (163) 7093 41 (173) 7097 47 (151) 7181 43 (167) 7261 53 (137) 7267 13 43 7339 41 (179) 7367 53 (139) 7379 47 (157) 7439 43 (173) 7473 3 47 53 7661 47 (163) 7849 47 (167) 7897 53 (149) 7943 13 47 8003 53 (151) 8131 47 (173) 8321 53 (157) 8413 47 (179) 8507 47 (181) 8639 53 (163) 8851 53 (167) 8957 13 53 9169 53 (173) 9487 53 (179) 9593 53 (181) 10123 53 (191) 10229 53 (193) 10441 53 (197) ---------------------------------------------------------------------------------- a17 <= 1363577, max Prime = 59, # of terms = 337 Terms 17,19,23,29,31,37,41,43,47,53,59,247,265,287,289,295,299,301,319,323,329,341,361,371,377,391,403,407,413,437,451,473,481,493,517,527,529,533,551,559,583,589,611,629,649,667,689,697,703,713,731,767,779,799,817,841,851,893,899,901,943,961,989,1003,1007,1037,1073,1081,1121,1139,1147,1159,1189,1207,1219,1247,1271,1273,1325,1333,1349,1357,1363,1369,1387,1403,1457,1475,1501,1517,1537,1541,1577,1591,1633,1643,1679,1681,1711,1739,1763,1769,1817,1829,1849,1891,1909,1927,1943,1961,2021,2047,2059,2077,2117,2173,2183,2201,2209,2231,2257,2263,2279,2291,2323,2369,2407,2419,2449,2479,2491,2501,2537,2573,2581,2597,2623,2627,2701,2747,2759,2773,2809,2813,2867,2881,2891,2911,2923,2929,2987,2993,3007,3053,3071,3103,3127,3131,3139,3149,3161,3193,3233,3239,3277,3293,3317,3337,3379,3397,3403,3431,3481,3503,3551,3569,3589,3599,3649,3683,3713,3737,3763,3799,3811,3827,3869,3901,3937,3953,3959,3977,4033,4061,4141,4171,4181,4183,4187,4189,4223,4247,4307,4309,4343,4387,4399,4429,4469,4559,4601,4633,4661,4687,4699,4717,4747,4841,4847,4859,4897,5015,5029,5069,5123,5141,5143,5207,5251,5311,5353,5371,5459,5461,5513,5546,5587,5617,5633,5671,5687,5699,5723,5777,5809,5891,5959,5969,5977,5989,6031,6077,6109,6157,6179,6191,6254,6313,6401,6407,6413,6431,6437,6439,6493,6533,6667,6683,6731,6751,6847,6943,7003,7009,7093,7097,7139,7181,7261,7339,7367,7379,7421,7439,7493,7611,7661,7697,7729,7783,7831,7849,7897,8003,8083,8131,8201,8213,8299,8319,8321,8413,8507,8639,8791,8851,8909,8957,8977,9071,9169,9259,9263,9353,9381,9487,9593,9617,9853,9971,10123,10207,10229,10441,10547,10561,10679,11183,11269,11387,11623,11741,11819,12449,13039,13157,13393 1 17 2 19 3 23 4 29 5 31 6 37 7 41 8 43 9 47 10 53 11 59 12 247 13 265 14 287 15 289 16 295 17 299 18 301 19 319 20 323 21 329 22 341 23 361 24 371 25 377 26 391 27 403 28 407 29 413 30 437 31 451 32 473 33 481 34 493 35 517 36 527 37 529 38 533 39 551 40 559 41 583 42 589 43 611 44 629 45 649 46 667 47 689 48 697 49 703 50 713 51 731 52 767 53 779 54 799 55 817 56 841 57 851 58 893 59 899 60 901 61 943 62 961 63 989 64 1003 65 1007 66 1037 67 1073 68 1081 69 1121 70 1139 71 1147 72 1159 73 1189 74 1207 75 1219 76 1247 77 1271 78 1273 79 1325 80 1333 81 1349 82 1357 83 1363 84 1369 85 1387 86 1403 87 1457 88 1475 89 1501 90 1517 91 1537 92 1541 93 1577 94 1591 95 1633 96 1643 97 1679 98 1681 99 1711 100 1739 101 1763 102 1769 103 1817 104 1829 105 1849 106 1891 107 1909 108 1927 109 1943 110 1961 111 2021 112 2047 113 2059 114 2077 115 2117 116 2173 117 2183 118 2201 119 2209 120 2231 121 2257 122 2263 123 2279 124 2291 125 2323 126 2369 127 2407 128 2419 129 2449 130 2479 131 2491 132 2501 133 2537 134 2573 135 2581 136 2597 137 2623 138 2627 139 2701 140 2747 141 2759 142 2773 143 2809 144 2813 145 2867 146 2881 147 2891 148 2911 149 2923 150 2929 151 2987 152 2993 153 3007 154 3053 155 3071 156 3103 157 3127 158 3131 159 3139 160 3149 161 3161 162 3193 163 3233 164 3239 165 3277 166 3293 167 3317 168 3337 169 3379 170 3397 171 3403 172 3431 173 3481 174 3503 175 3551 176 3569 177 3589 178 3599 179 3649 180 3683 181 3713 182 3737 183 3763 184 3799 185 3811 186 3827 187 3869 188 3901 189 3937 190 3953 191 3959 192 3977 193 4033 194 4061 195 4141 196 4171 197 4181 198 4183 199 4187 200 4189 201 4223 202 4247 203 4307 204 4309 205 4343 206 4387 207 4399 208 4429 209 4469 210 4559 211 4601 212 4633 213 4661 214 4687 215 4699 216 4717 217 4747 218 4841 219 4847 220 4859 221 4897 222 5015 223 5029 224 5069 225 5123 226 5141 227 5143 228 5207 229 5251 230 5311 231 5353 232 5371 233 5459 234 5461 235 5513 236 5546 237 5587 238 5617 239 5633 240 5671 241 5687 242 5699 243 5723 244 5777 245 5809 246 5891 247 5959 248 5969 249 5977 250 5989 251 6031 252 6077 253 6109 254 6157 255 6179 256 6191 257 6254 258 6313 259 6401 260 6407 261 6413 262 6431 263 6437 264 6439 265 6493 266 6533 267 6667 268 6683 269 6731 270 6751 271 6847 272 6943 273 7003 274 7009 275 7093 276 7097 277 7139 278 7181 279 7261 280 7339 281 7367 282 7379 283 7421 284 7439 285 7493 286 7611 287 7661 288 7697 289 7729 290 7783 291 7831 292 7849 293 7897 294 8003 295 8083 296 8131 297 8201 298 8213 299 8299 300 8319 301 8321 302 8413 303 8507 304 8639 305 8791 306 8851 307 8909 308 8957 309 8977 310 9071 311 9169 312 9259 313 9263 314 9353 315 9381 316 9487 317 9593 318 9617 319 9853 320 9971 321 10123 322 10207 323 10229 324 10441 325 10547 326 10561 327 10679 328 11183 329 11269 330 11387 331 11623 332 11741 333 11819 334 12449 335 13039 336 13157 337 13393 Primes contained in the terms 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 ==================================================== 17 17 19 19 23 23 29 29 31 31 37 37 41 41 43 43 47 47 53 53 59 59 247 13 19 265 5 53 287 7 41 289 17 295 5 59 299 13 23 301 7 43 319 11 29 323 17 19 329 7 47 341 11 31 361 19 371 7 53 377 13 29 391 17 23 403 13 31 407 11 37 413 7 59 437 19 23 451 11 41 473 11 43 481 13 37 493 17 29 517 11 47 527 17 31 529 23 533 13 41 551 19 29 559 13 43 583 11 53 589 19 31 611 13 47 629 17 37 649 11 59 667 23 29 689 13 53 697 17 41 703 19 37 713 23 31 731 17 43 767 13 59 779 19 41 799 17 47 817 19 43 841 29 851 23 37 893 19 47 899 29 31 901 17 53 943 23 41 961 31 989 23 43 1003 17 59 1007 19 53 1037 17 (61) 1073 29 37 1081 23 47 1121 19 59 1139 17 (67) 1147 31 37 1159 19 (61) 1189 29 41 1207 17 (71) 1219 23 53 1247 29 43 1271 31 41 1273 19 (67) 1325 5 53 1333 31 43 1349 19 (71) 1357 23 59 1363 29 47 1369 37 1387 19 (73) 1403 23 (61) 1457 31 47 1475 5 59 1501 19 (79) 1517 37 41 1537 29 53 1541 23 (67) 1577 19 (83) 1591 37 43 1633 23 (71) 1643 31 53 1679 23 (73) 1681 41 1711 29 59 1739 37 47 1763 41 43 1769 29 (61) 1817 23 (79) 1829 31 59 1849 43 1891 31 (61) 1909 23 (83) 1927 41 47 1943 29 (67) 1961 37 53 2021 43 47 2047 23 (89) 2059 29 (71) 2077 31 (67) 2117 29 (73) 2173 41 53 2183 37 59 2201 31 (71) 2209 47 2231 23 (97) 2257 37 (61) 2263 31 (73) 2279 43 53 2291 29 (79) 2323 23 (101) 2369 23 (103) 2407 29 (83) 2419 41 59 2449 31 (79) 2479 37 (67) 2491 47 53 2501 41 (61) 2537 43 59 2573 31 (83) 2581 29 (89) 2597 7 53 2623 43 (61) 2627 37 (71) 2701 37 (73) 2747 41 (67) 2759 31 (89) 2773 47 59 2809 53 2813 29 (97) 2867 47 (61) 2881 43 (67) 2891 7 59 2911 41 (71) 2923 37 (79) 2929 29 (101) 2987 29 (103) 2993 41 (73) 3007 31 (97) 3053 43 (71) 3071 37 (83) 3103 29 (107) 3127 53 59 3131 31 (101) 3139 43 (73) 3149 47 (67) 3161 29 (109) 3193 31 (103) 3233 53 (61) 3239 41 (79) 3277 29 (113) 3293 37 (89) 3317 31 (107) 3337 47 (71) 3379 31 (109) 3397 43 (79) 3403 41 (83) 3431 47 (73) 3481 59 3503 31 (113) 3551 53 (67) 3569 43 (83) 3589 37 (97) 3599 59 (61) 3649 41 (89) 3683 29 (127) 3713 47 (79) 3737 37 (101) 3763 53 (71) 3799 29 (131) 3811 37 (103) 3827 43 (89) 3869 53 (73) 3901 47 (83) 3937 31 (127) 3953 59 (67) 3959 37 (107) 3977 41 (97) 4033 37 (109) 4061 31 (131) 4141 41 (101) 4171 43 (97) 4181 37 (113) 4183 47 (89) 4187 53 (79) 4189 59 (71) 4223 41 (103) 4247 31 (137) 4307 59 (73) 4309 31 (139) 4343 43 (101) 4387 41 (107) 4399 53 (83) 4429 43 (103) 4469 41 (109) 4559 47 (97) 4601 43 (107) 4633 41 (113) 4661 59 (79) 4687 43 (109) 4699 37 (127) 4717 53 (89) 4747 47 (101) 4841 47 (103) 4847 37 (131) 4859 43 (113) 4897 59 (83) 5015 5 17 59 5029 47 (107) 5069 37 (137) 5123 47 (109) 5141 53 (97) 5143 37 (139) 5207 41 (127) 5251 59 (89) 5311 47 (113) 5353 53 (101) 5371 41 (131) 5459 53 (103) 5461 43 (127) 5513 37 (149) 5546 2 47 59 5587 37 (151) 5617 41 (137) 5633 43 (131) 5671 53 (107) 5687 11 47 5699 41 (139) 5723 59 (97) 5777 53 (109) 5809 37 (157) 5891 43 (137) 5959 59 (101) 5969 47 (127) 5977 43 (139) 5989 53 (113) 6031 37 (163) 6077 59 (103) 6109 41 (149) 6157 47 (131) 6179 37 (167) 6191 41 (151) 6254 2 53 59 6313 59 (107) 6401 37 (173) 6407 43 (149) 6413 11 53 6431 59 (109) 6437 41 (157) 6439 47 (137) 6493 43 (151) 6533 47 (139) 6667 59 (113) 6683 41 (163) 6731 53 (127) 6751 43 (157) 6847 41 (167) 6943 53 (131) 7003 47 (149) 7009 43 (163) 7093 41 (173) 7097 47 (151) 7139 11 59 7181 43 (167) 7261 53 (137) 7339 41 (179) 7367 53 (139) 7379 47 (157) 7421 41 (181) 7439 43 (173) 7493 59 (127) 7611 3 43 59 7661 47 (163) 7697 43 (179) 7729 59 (131) 7783 43 (181) 7831 41 (191) 7849 47 (167) 7897 53 (149) 8003 53 (151) 8083 59 (137) 8131 47 (173) 8201 59 (139) 8213 43 (191) 8299 43 (193) 8319 3 47 59 8321 53 (157) 8413 47 (179) 8507 47 (181) 8639 53 (163) 8791 59 (149) 8851 53 (167) 8909 59 (151) 8957 13 53 8977 47 (191) 9071 47 (193) 9169 53 (173) 9259 47 (197) 9263 59 (157) 9353 47 (199) 9381 3 53 59 9487 53 (179) 9593 53 (181) 9617 59 (163) 9853 59 (167) 9971 13 59 10123 53 (191) 10207 59 (173) 10229 53 (193) 10441 53 (197) 10547 53 (199) 10561 59 (179) 10679 59 (181) 11183 53 (211) 11269 59 (191) 11387 59 (193) 11623 59 (197) 11741 59 (199) 11819 53 (223) 12449 59 (211) 13039 13 17 59 13157 59 (223) 13393 59 (227) ---------------------------------------------------------------------------------- a18 <= 1830468, max Prime = 61, # of terms = 388 Terms 17,19,23,29,31,37,41,43,47,53,59,61,265,289,295,305,323,329,361,371,377,391,403,407,413,427,437,451,473,481,493,517,527,529,533,551,559,583,589,611,629,649,667,671,689,697,703,713,731,767,779,793,799,817,841,851,893,899,901,943,961,989,1003,1007,1037,1073,1081,1121,1139,1147,1159,1189,1207,1219,1241,1247,1271,1273,1333,1349,1357,1363,1369,1387,1403,1457,1475,1501,1517,1525,1537,1541,1577,1591,1633,1643,1679,1681,1691,1711,1739,1763,1769,1817,1829,1849,1891,1909,1927,1943,1961,2021,2047,2059,2077,2117,2173,2183,2201,2209,2231,2257,2263,2279,2291,2323,2369,2407,2419,2449,2461,2479,2491,2501,2537,2573,2581,2597,2623,2627,2701,2747,2759,2773,2809,2813,2867,2881,2891,2911,2923,2929,2987,2989,2993,3007,3053,3071,3103,3127,3131,3139,3149,3161,3193,3233,3239,3277,3293,3317,3337,3379,3397,3403,3431,3481,3503,3551,3569,3589,3599,3649,3683,3713,3721,3737,3763,3799,3811,3827,3869,3901,3937,3953,3959,3973,3977,4033,4061,4087,4141,4171,4181,4183,4187,4189,4223,4247,4307,4309,4331,4343,4387,4399,4429,4453,4469,4559,4601,4619,4633,4661,4687,4699,4717,4747,4819,4841,4847,4859,4897,5029,5063,5069,5123,5141,5143,5207,5251,5311,5353,5371,5429,5459,5461,5513,5587,5617,5633,5671,5687,5699,5723,5777,5809,5891,5917,5959,5969,5977,5989,6031,6077,6109,6157,6161,6179,6191,6283,6313,6401,6407,6413,6431,6437,6439,6466,6493,6527,6533,6649,6667,6683,6731,6751,6847,6893,6943,7003,7009,7093,7097,7139,7181,7198,7261,7339,7367,7379,7381,7421,7439,7493,7661,7697,7729,7747,7783,7831,7849,7897,7913,7991,8003,8083,8131,8201,8213,8299,8321,8357,8413,8471,8479,8507,8557,8639,8791,8851,8909,8957,8977,9071,9089,9169,9211,9259,9263,9353,9381,9487,9577,9593,9617,9699,9853,9917,9943,9971,10123,10187,10207,10229,10309,10441,10481,10547,10553,10561,10679,10797,10919,11041,11183,11269,11387,11623,11651,11741,11773,11819,12017,12139,12449,12871,13157,13393,13481,13511,13603,13747,13847,13969,14101,14213,14219,14579,14701 1 17 2 19 3 23 4 29 5 31 6 37 7 41 8 43 9 47 10 53 11 59 12 61 13 265 14 289 15 295 16 305 17 323 18 329 19 361 20 371 21 377 22 391 23 403 24 407 25 413 26 427 27 437 28 451 29 473 30 481 31 493 32 517 33 527 34 529 35 533 36 551 37 559 38 583 39 589 40 611 41 629 42 649 43 667 44 671 45 689 46 697 47 703 48 713 49 731 50 767 51 779 52 793 53 799 54 817 55 841 56 851 57 893 58 899 59 901 60 943 61 961 62 989 63 1003 64 1007 65 1037 66 1073 67 1081 68 1121 69 1139 70 1147 71 1159 72 1189 73 1207 74 1219 75 1241 76 1247 77 1271 78 1273 79 1333 80 1349 81 1357 82 1363 83 1369 84 1387 85 1403 86 1457 87 1475 88 1501 89 1517 90 1525 91 1537 92 1541 93 1577 94 1591 95 1633 96 1643 97 1679 98 1681 99 1691 100 1711 101 1739 102 1763 103 1769 104 1817 105 1829 106 1849 107 1891 108 1909 109 1927 110 1943 111 1961 112 2021 113 2047 114 2059 115 2077 116 2117 117 2173 118 2183 119 2201 120 2209 121 2231 122 2257 123 2263 124 2279 125 2291 126 2323 127 2369 128 2407 129 2419 130 2449 131 2461 132 2479 133 2491 134 2501 135 2537 136 2573 137 2581 138 2597 139 2623 140 2627 141 2701 142 2747 143 2759 144 2773 145 2809 146 2813 147 2867 148 2881 149 2891 150 2911 151 2923 152 2929 153 2987 154 2989 155 2993 156 3007 157 3053 158 3071 159 3103 160 3127 161 3131 162 3139 163 3149 164 3161 165 3193 166 3233 167 3239 168 3277 169 3293 170 3317 171 3337 172 3379 173 3397 174 3403 175 3431 176 3481 177 3503 178 3551 179 3569 180 3589 181 3599 182 3649 183 3683 184 3713 185 3721 186 3737 187 3763 188 3799 189 3811 190 3827 191 3869 192 3901 193 3937 194 3953 195 3959 196 3973 197 3977 198 4033 199 4061 200 4087 201 4141 202 4171 203 4181 204 4183 205 4187 206 4189 207 4223 208 4247 209 4307 210 4309 211 4331 212 4343 213 4387 214 4399 215 4429 216 4453 217 4469 218 4559 219 4601 220 4619 221 4633 222 4661 223 4687 224 4699 225 4717 226 4747 227 4819 228 4841 229 4847 230 4859 231 4897 232 5029 233 5063 234 5069 235 5123 236 5141 237 5143 238 5207 239 5251 240 5311 241 5353 242 5371 243 5429 244 5459 245 5461 246 5513 247 5587 248 5617 249 5633 250 5671 251 5687 252 5699 253 5723 254 5777 255 5809 256 5891 257 5917 258 5959 259 5969 260 5977 261 5989 262 6031 263 6077 264 6109 265 6157 266 6161 267 6179 268 6191 269 6283 270 6313 271 6401 272 6407 273 6413 274 6431 275 6437 276 6439 277 6466 278 6493 279 6527 280 6533 281 6649 282 6667 283 6683 284 6731 285 6751 286 6847 287 6893 288 6943 289 7003 290 7009 291 7093 292 7097 293 7139 294 7181 295 7198 296 7261 297 7339 298 7367 299 7379 300 7381 301 7421 302 7439 303 7493 304 7661 305 7697 306 7729 307 7747 308 7783 309 7831 310 7849 311 7897 312 7913 313 7991 314 8003 315 8083 316 8131 317 8201 318 8213 319 8299 320 8321 321 8357 322 8413 323 8471 324 8479 325 8507 326 8557 327 8639 328 8791 329 8851 330 8909 331 8957 332 8977 333 9071 334 9089 335 9169 336 9211 337 9259 338 9263 339 9353 340 9381 341 9487 342 9577 343 9593 344 9617 345 9699 346 9853 347 9917 348 9943 349 9971 350 10123 351 10187 352 10207 353 10229 354 10309 355 10441 356 10481 357 10547 358 10553 359 10561 360 10679 361 10797 362 10919 363 11041 364 11183 365 11269 366 11387 367 11623 368 11651 369 11741 370 11773 371 11819 372 12017 373 12139 374 12449 375 12871 376 13157 377 13393 378 13481 379 13511 380 13603 381 13747 382 13847 383 13969 384 14101 385 14213 386 14219 387 14579 388 14701 Primes contained in the terms 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 ======================================================= 17 17 19 19 23 23 29 29 31 31 37 37 41 41 43 43 47 47 53 53 59 59 61 61 265 5 53 289 17 295 5 59 305 5 61 323 17 19 329 7 47 361 19 371 7 53 377 13 29 391 17 23 403 13 31 407 11 37 413 7 59 427 7 61 437 19 23 451 11 41 473 11 43 481 13 37 493 17 29 517 11 47 527 17 31 529 23 533 13 41 551 19 29 559 13 43 583 11 53 589 19 31 611 13 47 629 17 37 649 11 59 667 23 29 671 11 61 689 13 53 697 17 41 703 19 37 713 23 31 731 17 43 767 13 59 779 19 41 793 13 61 799 17 47 817 19 43 841 29 851 23 37 893 19 47 899 29 31 901 17 53 943 23 41 961 31 989 23 43 1003 17 59 1007 19 53 1037 17 61 1073 29 37 1081 23 47 1121 19 59 1139 17 (67) 1147 31 37 1159 19 61 1189 29 41 1207 17 (71) 1219 23 53 1241 17 (73) 1247 29 43 1271 31 41 1273 19 (67) 1333 31 43 1349 19 (71) 1357 23 59 1363 29 47 1369 37 1387 19 (73) 1403 23 61 1457 31 47 1475 5 59 1501 19 (79) 1517 37 41 1525 5 61 1537 29 53 1541 23 (67) 1577 19 (83) 1591 37 43 1633 23 (71) 1643 31 53 1679 23 (73) 1681 41 1691 19 (89) 1711 29 59 1739 37 47 1763 41 43 1769 29 61 1817 23 (79) 1829 31 59 1849 43 1891 31 61 1909 23 (83) 1927 41 47 1943 29 (67) 1961 37 53 2021 43 47 2047 23 (89) 2059 29 (71) 2077 31 (67) 2117 29 (73) 2173 41 53 2183 37 59 2201 31 (71) 2209 47 2231 23 (97) 2257 37 61 2263 31 (73) 2279 43 53 2291 29 (79) 2323 23 (101) 2369 23 (103) 2407 29 (83) 2419 41 59 2449 31 (79) 2461 23 (107) 2479 37 (67) 2491 47 53 2501 41 61 2537 43 59 2573 31 (83) 2581 29 (89) 2597 7 53 2623 43 61 2627 37 (71) 2701 37 (73) 2747 41 (67) 2759 31 (89) 2773 47 59 2809 53 2813 29 (97) 2867 47 61 2881 43 (67) 2891 7 59 2911 41 (71) 2923 37 (79) 2929 29 (101) 2987 29 (103) 2989 7 61 2993 41 (73) 3007 31 (97) 3053 43 (71) 3071 37 (83) 3103 29 (107) 3127 53 59 3131 31 (101) 3139 43 (73) 3149 47 (67) 3161 29 (109) 3193 31 (103) 3233 53 61 3239 41 (79) 3277 29 (113) 3293 37 (89) 3317 31 (107) 3337 47 (71) 3379 31 (109) 3397 43 (79) 3403 41 (83) 3431 47 (73) 3481 59 3503 31 (113) 3551 53 (67) 3569 43 (83) 3589 37 (97) 3599 59 61 3649 41 (89) 3683 29 (127) 3713 47 (79) 3721 61 3737 37 (101) 3763 53 (71) 3799 29 (131) 3811 37 (103) 3827 43 (89) 3869 53 (73) 3901 47 (83) 3937 31 (127) 3953 59 (67) 3959 37 (107) 3973 29 (137) 3977 41 (97) 4033 37 (109) 4061 31 (131) 4087 61 (67) 4141 41 (101) 4171 43 (97) 4181 37 (113) 4183 47 (89) 4187 53 (79) 4189 59 (71) 4223 41 (103) 4247 31 (137) 4307 59 (73) 4309 31 (139) 4331 61 (71) 4343 43 (101) 4387 41 (107) 4399 53 (83) 4429 43 (103) 4453 61 (73) 4469 41 (109) 4559 47 (97) 4601 43 (107) 4619 31 (149) 4633 41 (113) 4661 59 (79) 4687 43 (109) 4699 37 (127) 4717 53 (89) 4747 47 (101) 4819 61 (79) 4841 47 (103) 4847 37 (131) 4859 43 (113) 4897 59 (83) 5029 47 (107) 5063 61 (83) 5069 37 (137) 5123 47 (109) 5141 53 (97) 5143 37 (139) 5207 41 (127) 5251 59 (89) 5311 47 (113) 5353 53 (101) 5371 41 (131) 5429 61 (89) 5459 53 (103) 5461 43 (127) 5513 37 (149) 5587 37 (151) 5617 41 (137) 5633 43 (131) 5671 53 (107) 5687 11 47 5699 41 (139) 5723 59 (97) 5777 53 (109) 5809 37 (157) 5891 43 (137) 5917 61 (97) 5959 59 (101) 5969 47 (127) 5977 43 (139) 5989 53 (113) 6031 37 (163) 6077 59 (103) 6109 41 (149) 6157 47 (131) 6161 61 (101) 6179 37 (167) 6191 41 (151) 6283 61 (103) 6313 59 (107) 6401 37 (173) 6407 43 (149) 6413 11 53 6431 59 (109) 6437 41 (157) 6439 47 (137) 6466 2 53 61 6493 43 (151) 6527 61 (107) 6533 47 (139) 6649 61 (109) 6667 59 (113) 6683 41 (163) 6731 53 (127) 6751 43 (157) 6847 41 (167) 6893 61 (113) 6943 53 (131) 7003 47 (149) 7009 43 (163) 7093 41 (173) 7097 47 (151) 7139 11 59 7181 43 (167) 7198 2 59 61 7261 53 (137) 7339 41 (179) 7367 53 (139) 7379 47 (157) 7381 11 61 7421 41 (181) 7439 43 (173) 7493 59 (127) 7661 47 (163) 7697 43 (179) 7729 59 (131) 7747 61 (127) 7783 43 (181) 7831 41 (191) 7849 47 (167) 7897 53 (149) 7913 41 (193) 7991 61 (131) 8003 53 (151) 8083 59 (137) 8131 47 (173) 8201 59 (139) 8213 43 (191) 8299 43 (193) 8321 53 (157) 8357 61 (137) 8413 47 (179) 8471 43 (197) 8479 61 (139) 8507 47 (181) 8557 43 (199) 8639 53 (163) 8791 59 (149) 8851 53 (167) 8909 59 (151) 8957 13 53 8977 47 (191) 9071 47 (193) 9089 61 (149) 9169 53 (173) 9211 61 (151) 9259 47 (197) 9263 59 (157) 9353 47 (199) 9381 3 53 59 9487 53 (179) 9577 61 (157) 9593 53 (181) 9617 59 (163) 9699 3 53 61 9853 59 (167) 9917 47 (211) 9943 61 (163) 9971 13 59 10123 53 (191) 10187 61 (167) 10207 59 (173) 10229 53 (193) 10309 13 61 10441 53 (197) 10481 47 (223) 10547 53 (199) 10553 61 (173) 10561 59 (179) 10679 59 (181) 10797 3 59 61 10919 61 (179) 11041 61 (181) 11183 53 (211) 11269 59 (191) 11387 59 (193) 11623 59 (197) 11651 61 (191) 11741 59 (199) 11773 61 (193) 11819 53 (223) 12017 61 (197) 12139 61 (199) 12449 59 (211) 12871 61 (211) 13157 59 (223) 13393 59 (227) 13481 13 17 61 13511 59 (229) 13603 61 (223) 13747 59 (233) 13847 61 (227) 13969 61 (229) 14101 59 (239) 14213 61 (233) 14219 59 (241) 14579 61 (239) 14701 61 (241) ---------------------------------------------------------------------------------- a19 <= 2461758, max Prime = 67, # of terms = 442 Terms 17,19,23,29,31,37,41,43,47,53,59,61,67,289,295,305,323,335,361,371,391,413,427,437,451,469,473,481,493,517,527,529,533,551,559,583,589,611,629,649,667,671,689,697,703,713,731,737,767,779,793,799,817,841,851,871,893,899,901,943,961,989,1003,1007,1037,1073,1081,1121,1139,1147,1159,1189,1207,1219,1247,1271,1273,1333,1349,1357,1363,1369,1387,1403,1457,1501,1517,1525,1537,1541,1577,1591,1633,1643,1675,1679,1681,1691,1711,1739,1763,1769,1817,1829,1849,1891,1909,1927,1943,1961,2021,2047,2059,2077,2117,2173,2183,2201,2209,2231,2257,2263,2279,2291,2323,2369,2407,2419,2449,2461,2479,2491,2501,2537,2573,2581,2623,2627,2701,2747,2759,2773,2809,2813,2867,2881,2891,2911,2923,2929,2987,2989,2993,3007,3053,3071,3103,3127,3131,3139,3149,3161,3193,3233,3239,3277,3283,3293,3317,3337,3379,3397,3403,3431,3481,3503,3551,3569,3589,3599,3649,3683,3713,3721,3737,3763,3799,3811,3827,3869,3901,3937,3953,3959,3973,3977,4031,4033,4061,4087,4141,4171,4181,4183,4187,4189,4223,4247,4307,4309,4331,4343,4387,4399,4429,4453,4469,4489,4559,4601,4619,4633,4661,4681,4687,4699,4717,4747,4757,4819,4841,4847,4859,4891,4897,5029,5063,5069,5123,5141,5143,5207,5251,5293,5311,5353,5371,5429,5459,5461,5513,5561,5587,5617,5633,5671,5699,5723,5777,5809,5891,5917,5959,5963,5969,5977,5989,6031,6077,6109,6157,6161,6179,6191,6283,6313,6401,6407,6431,6437,6439,6493,6499,6527,6533,6623,6649,6667,6683,6731,6751,6767,6847,6893,6901,6943,7003,7009,7093,7097,7139,7169,7181,7261,7303,7339,7367,7379,7381,7421,7439,7493,7571,7661,7697,7729,7747,7783,7831,7849,7897,7906,7913,7991,8003,8083,8107,8131,8174,8201,8213,8299,8321,8357,8413,8471,8479,8507,8509,8557,8639,8777,8791,8851,8909,8957,8977,9071,9089,9169,9179,9211,9259,9263,9313,9353,9487,9577,9593,9617,9853,9917,9943,9971,9983,10117,10123,10187,10207,10229,10309,10441,10481,10519,10547,10553,10561,10653,10669,10679,10763,10919,10921,11041,11183,11189,11269,11323,11387,11591,11623,11651,11741,11773,11819,11859,11993,12017,12031,12127,12137,12139,12261,12349,12449,12529,12667,12773,12797,12871,12931,13157,13199,13333,13393,13511,13603,13747,13847,13969,14101,14137,14213,14219,14579,14701,14807,14809,14941,15163,15209,15311,15343,15611,15677,16013,16043,16147,16817,17219,17621,18023 1 17 2 19 3 23 4 29 5 31 6 37 7 41 8 43 9 47 10 53 11 59 12 61 13 67 14 289 15 295 16 305 17 323 18 335 19 361 20 371 21 391 22 413 23 427 24 437 25 451 26 469 27 473 28 481 29 493 30 517 31 527 32 529 33 533 34 551 35 559 36 583 37 589 38 611 39 629 40 649 41 667 42 671 43 689 44 697 45 703 46 713 47 731 48 737 49 767 50 779 51 793 52 799 53 817 54 841 55 851 56 871 57 893 58 899 59 901 60 943 61 961 62 989 63 1003 64 1007 65 1037 66 1073 67 1081 68 1121 69 1139 70 1147 71 1159 72 1189 73 1207 74 1219 75 1247 76 1271 77 1273 78 1333 79 1349 80 1357 81 1363 82 1369 83 1387 84 1403 85 1457 86 1501 87 1517 88 1525 89 1537 90 1541 91 1577 92 1591 93 1633 94 1643 95 1675 96 1679 97 1681 98 1691 99 1711 100 1739 101 1763 102 1769 103 1817 104 1829 105 1849 106 1891 107 1909 108 1927 109 1943 110 1961 111 2021 112 2047 113 2059 114 2077 115 2117 116 2173 117 2183 118 2201 119 2209 120 2231 121 2257 122 2263 123 2279 124 2291 125 2323 126 2369 127 2407 128 2419 129 2449 130 2461 131 2479 132 2491 133 2501 134 2537 135 2573 136 2581 137 2623 138 2627 139 2701 140 2747 141 2759 142 2773 143 2809 144 2813 145 2867 146 2881 147 2891 148 2911 149 2923 150 2929 151 2987 152 2989 153 2993 154 3007 155 3053 156 3071 157 3103 158 3127 159 3131 160 3139 161 3149 162 3161 163 3193 164 3233 165 3239 166 3277 167 3283 168 3293 169 3317 170 3337 171 3379 172 3397 173 3403 174 3431 175 3481 176 3503 177 3551 178 3569 179 3589 180 3599 181 3649 182 3683 183 3713 184 3721 185 3737 186 3763 187 3799 188 3811 189 3827 190 3869 191 3901 192 3937 193 3953 194 3959 195 3973 196 3977 197 4031 198 4033 199 4061 200 4087 201 4141 202 4171 203 4181 204 4183 205 4187 206 4189 207 4223 208 4247 209 4307 210 4309 211 4331 212 4343 213 4387 214 4399 215 4429 216 4453 217 4469 218 4489 219 4559 220 4601 221 4619 222 4633 223 4661 224 4681 225 4687 226 4699 227 4717 228 4747 229 4757 230 4819 231 4841 232 4847 233 4859 234 4891 235 4897 236 5029 237 5063 238 5069 239 5123 240 5141 241 5143 242 5207 243 5251 244 5293 245 5311 246 5353 247 5371 248 5429 249 5459 250 5461 251 5513 252 5561 253 5587 254 5617 255 5633 256 5671 257 5699 258 5723 259 5777 260 5809 261 5891 262 5917 263 5959 264 5963 265 5969 266 5977 267 5989 268 6031 269 6077 270 6109 271 6157 272 6161 273 6179 274 6191 275 6283 276 6313 277 6401 278 6407 279 6431 280 6437 281 6439 282 6493 283 6499 284 6527 285 6533 286 6623 287 6649 288 6667 289 6683 290 6731 291 6751 292 6767 293 6847 294 6893 295 6901 296 6943 297 7003 298 7009 299 7093 300 7097 301 7139 302 7169 303 7181 304 7261 305 7303 306 7339 307 7367 308 7379 309 7381 310 7421 311 7439 312 7493 313 7571 314 7661 315 7697 316 7729 317 7747 318 7783 319 7831 320 7849 321 7897 322 7906 323 7913 324 7991 325 8003 326 8083 327 8107 328 8131 329 8174 330 8201 331 8213 332 8299 333 8321 334 8357 335 8413 336 8471 337 8479 338 8507 339 8509 340 8557 341 8639 342 8777 343 8791 344 8851 345 8909 346 8957 347 8977 348 9071 349 9089 350 9169 351 9179 352 9211 353 9259 354 9263 355 9313 356 9353 357 9487 358 9577 359 9593 360 9617 361 9853 362 9917 363 9943 364 9971 365 9983 366 10117 367 10123 368 10187 369 10207 370 10229 371 10309 372 10441 373 10481 374 10519 375 10547 376 10553 377 10561 378 10653 379 10669 380 10679 381 10763 382 10919 383 10921 384 11041 385 11183 386 11189 387 11269 388 11323 389 11387 390 11591 391 11623 392 11651 393 11741 394 11773 395 11819 396 11859 397 11993 398 12017 399 12031 400 12127 401 12137 402 12139 403 12261 404 12349 405 12449 406 12529 407 12667 408 12773 409 12797 410 12871 411 12931 412 13157 413 13199 414 13333 415 13393 416 13511 417 13603 418 13747 419 13847 420 13969 421 14101 422 14137 423 14213 424 14219 425 14579 426 14701 427 14807 428 14809 429 14941 430 15163 431 15209 432 15311 433 15343 434 15611 435 15677 436 16013 437 16043 438 16147 439 16817 440 17219 441 17621 442 18023 Primes contained in the terms 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 ========================================================== 17 17 19 19 23 23 29 29 31 31 37 37 41 41 43 43 47 47 53 53 59 59 61 61 67 67 289 17 295 5 59 305 5 61 323 17 19 335 5 67 361 19 371 7 53 391 17 23 413 7 59 427 7 61 437 19 23 451 11 41 469 7 67 473 11 43 481 13 37 493 17 29 517 11 47 527 17 31 529 23 533 13 41 551 19 29 559 13 43 583 11 53 589 19 31 611 13 47 629 17 37 649 11 59 667 23 29 671 11 61 689 13 53 697 17 41 703 19 37 713 23 31 731 17 43 737 11 67 767 13 59 779 19 41 793 13 61 799 17 47 817 19 43 841 29 851 23 37 871 13 67 893 19 47 899 29 31 901 17 53 943 23 41 961 31 989 23 43 1003 17 59 1007 19 53 1037 17 61 1073 29 37 1081 23 47 1121 19 59 1139 17 67 1147 31 37 1159 19 61 1189 29 41 1207 17 (71) 1219 23 53 1247 29 43 1271 31 41 1273 19 67 1333 31 43 1349 19 (71) 1357 23 59 1363 29 47 1369 37 1387 19 (73) 1403 23 61 1457 31 47 1501 19 (79) 1517 37 41 1525 5 61 1537 29 53 1541 23 67 1577 19 (83) 1591 37 43 1633 23 (71) 1643 31 53 1675 5 67 1679 23 (73) 1681 41 1691 19 (89) 1711 29 59 1739 37 47 1763 41 43 1769 29 61 1817 23 (79) 1829 31 59 1849 43 1891 31 61 1909 23 (83) 1927 41 47 1943 29 67 1961 37 53 2021 43 47 2047 23 (89) 2059 29 (71) 2077 31 67 2117 29 (73) 2173 41 53 2183 37 59 2201 31 (71) 2209 47 2231 23 (97) 2257 37 61 2263 31 (73) 2279 43 53 2291 29 (79) 2323 23 (101) 2369 23 (103) 2407 29 (83) 2419 41 59 2449 31 (79) 2461 23 (107) 2479 37 67 2491 47 53 2501 41 61 2537 43 59 2573 31 (83) 2581 29 (89) 2623 43 61 2627 37 (71) 2701 37 (73) 2747 41 67 2759 31 (89) 2773 47 59 2809 53 2813 29 (97) 2867 47 61 2881 43 67 2891 7 59 2911 41 (71) 2923 37 (79) 2929 29 (101) 2987 29 (103) 2989 7 61 2993 41 (73) 3007 31 (97) 3053 43 (71) 3071 37 (83) 3103 29 (107) 3127 53 59 3131 31 (101) 3139 43 (73) 3149 47 67 3161 29 (109) 3193 31 (103) 3233 53 61 3239 41 (79) 3277 29 (113) 3283 7 67 3293 37 (89) 3317 31 (107) 3337 47 (71) 3379 31 (109) 3397 43 (79) 3403 41 (83) 3431 47 (73) 3481 59 3503 31 (113) 3551 53 67 3569 43 (83) 3589 37 (97) 3599 59 61 3649 41 (89) 3683 29 (127) 3713 47 (79) 3721 61 3737 37 (101) 3763 53 (71) 3799 29 (131) 3811 37 (103) 3827 43 (89) 3869 53 (73) 3901 47 (83) 3937 31 (127) 3953 59 67 3959 37 (107) 3973 29 (137) 3977 41 (97) 4031 29 (139) 4033 37 (109) 4061 31 (131) 4087 61 67 4141 41 (101) 4171 43 (97) 4181 37 (113) 4183 47 (89) 4187 53 (79) 4189 59 (71) 4223 41 (103) 4247 31 (137) 4307 59 (73) 4309 31 (139) 4331 61 (71) 4343 43 (101) 4387 41 (107) 4399 53 (83) 4429 43 (103) 4453 61 (73) 4469 41 (109) 4489 67 4559 47 (97) 4601 43 (107) 4619 31 (149) 4633 41 (113) 4661 59 (79) 4681 31 (151) 4687 43 (109) 4699 37 (127) 4717 53 (89) 4747 47 (101) 4757 67 (71) 4819 61 (79) 4841 47 (103) 4847 37 (131) 4859 43 (113) 4891 67 (73) 4897 59 (83) 5029 47 (107) 5063 61 (83) 5069 37 (137) 5123 47 (109) 5141 53 (97) 5143 37 (139) 5207 41 (127) 5251 59 (89) 5293 67 (79) 5311 47 (113) 5353 53 (101) 5371 41 (131) 5429 61 (89) 5459 53 (103) 5461 43 (127) 5513 37 (149) 5561 67 (83) 5587 37 (151) 5617 41 (137) 5633 43 (131) 5671 53 (107) 5699 41 (139) 5723 59 (97) 5777 53 (109) 5809 37 (157) 5891 43 (137) 5917 61 (97) 5959 59 (101) 5963 67 (89) 5969 47 (127) 5977 43 (139) 5989 53 (113) 6031 37 (163) 6077 59 (103) 6109 41 (149) 6157 47 (131) 6161 61 (101) 6179 37 (167) 6191 41 (151) 6283 61 (103) 6313 59 (107) 6401 37 (173) 6407 43 (149) 6431 59 (109) 6437 41 (157) 6439 47 (137) 6493 43 (151) 6499 67 (97) 6527 61 (107) 6533 47 (139) 6623 37 (179) 6649 61 (109) 6667 59 (113) 6683 41 (163) 6731 53 (127) 6751 43 (157) 6767 67 (101) 6847 41 (167) 6893 61 (113) 6901 67 (103) 6943 53 (131) 7003 47 (149) 7009 43 (163) 7093 41 (173) 7097 47 (151) 7139 11 59 7169 67 (107) 7181 43 (167) 7261 53 (137) 7303 67 (109) 7339 41 (179) 7367 53 (139) 7379 47 (157) 7381 11 61 7421 41 (181) 7439 43 (173) 7493 59 (127) 7571 67 (113) 7661 47 (163) 7697 43 (179) 7729 59 (131) 7747 61 (127) 7783 43 (181) 7831 41 (191) 7849 47 (167) 7897 53 (149) 7906 2 59 67 7913 41 (193) 7991 61 (131) 8003 53 (151) 8083 59 (137) 8107 11 67 8131 47 (173) 8174 2 61 67 8201 59 (139) 8213 43 (191) 8299 43 (193) 8321 53 (157) 8357 61 (137) 8413 47 (179) 8471 43 (197) 8479 61 (139) 8507 47 (181) 8509 67 (127) 8557 43 (199) 8639 53 (163) 8777 67 (131) 8791 59 (149) 8851 53 (167) 8909 59 (151) 8957 13 53 8977 47 (191) 9071 47 (193) 9089 61 (149) 9169 53 (173) 9179 67 (137) 9211 61 (151) 9259 47 (197) 9263 59 (157) 9313 67 (139) 9353 47 (199) 9487 53 (179) 9577 61 (157) 9593 53 (181) 9617 59 (163) 9853 59 (167) 9917 47 (211) 9943 61 (163) 9971 13 59 9983 67 (149) 10117 67 (151) 10123 53 (191) 10187 61 (167) 10207 59 (173) 10229 53 (193) 10309 13 61 10441 53 (197) 10481 47 (223) 10519 67 (157) 10547 53 (199) 10553 61 (173) 10561 59 (179) 10653 3 53 67 10669 47 (227) 10679 59 (181) 10763 47 (229) 10919 61 (179) 10921 67 (163) 11041 61 (181) 11183 53 (211) 11189 67 (167) 11269 59 (191) 11323 13 67 11387 59 (193) 11591 67 (173) 11623 59 (197) 11651 61 (191) 11741 59 (199) 11773 61 (193) 11819 53 (223) 11859 3 59 67 11993 67 (179) 12017 61 (197) 12031 53 (227) 12127 67 (181) 12137 53 (229) 12139 61 (199) 12261 3 61 67 12349 53 (233) 12449 59 (211) 12529 11 17 67 12667 53 (239) 12773 53 (241) 12797 67 (191) 12871 61 (211) 12931 67 (193) 13157 59 (223) 13199 67 (197) 13333 67 (199) 13393 59 (227) 13511 59 (229) 13603 61 (223) 13747 59 (233) 13847 61 (227) 13969 61 (229) 14101 59 (239) 14137 67 (211) 14213 61 (233) 14219 59 (241) 14579 61 (239) 14701 61 (241) 14807 13 17 67 14809 59 (251) 14941 67 (223) 15163 59 (257) 15209 67 (227) 15311 61 (251) 15343 67 (229) 15611 67 (233) 15677 61 (257) 16013 67 (239) 16043 61 (263) 16147 67 (241) 16817 67 (251) 17219 67 (257) 17621 67 (263) 18023 67 (269) ---------------------------------------------------------------------------------- a20 <= 3229840, max Prime = 71, # of terms = 500 Terms 17,19,23,29,31,37,41,43,47,53,59,61,67,71,289,305,323,335,355,361,371,391,413,427,437,469,473,481,493,497,517,527,529,533,551,559,583,589,611,629,649,667,671,689,697,703,713,731,737,767,779,781,793,799,817,841,851,871,893,899,901,923,943,961,989,1003,1007,1037,1073,1081,1121,1139,1147,1159,1189,1207,1219,1247,1271,1273,1333,1349,1357,1363,1369,1387,1403,1457,1501,1517,1537,1541,1577,1591,1633,1643,1675,1679,1681,1691,1711,1739,1763,1769,1775,1817,1829,1849,1891,1909,1927,1943,1961,2021,2047,2059,2077,2117,2173,2183,2201,2209,2231,2257,2263,2279,2291,2323,2369,2407,2419,2449,2461,2479,2491,2501,2537,2573,2581,2623,2627,2701,2747,2759,2773,2809,2813,2867,2881,2911,2923,2929,2987,2993,3007,3053,3071,3103,3127,3131,3139,3149,3161,3193,3233,3239,3277,3283,3293,3317,3337,3379,3397,3403,3431,3479,3481,3503,3551,3569,3589,3599,3649,3683,3713,3721,3737,3763,3799,3811,3827,3869,3901,3937,3953,3959,3973,3977,4031,4033,4061,4087,4141,4171,4181,4183,4187,4189,4223,4247,4307,4309,4331,4343,4387,4399,4429,4453,4469,4489,4559,4601,4619,4633,4661,4681,4687,4699,4717,4747,4757,4819,4841,4847,4859,4891,4897,5029,5041,5063,5069,5123,5141,5143,5183,5207,5251,5293,5311,5353,5371,5429,5459,5461,5513,5561,5587,5609,5617,5633,5671,5699,5723,5777,5809,5891,5893,5917,5959,5963,5969,5977,5989,6031,6077,6109,6157,6161,6179,6191,6283,6313,6319,6401,6407,6431,6437,6439,6493,6499,6527,6533,6623,6649,6667,6683,6731,6751,6767,6847,6887,6893,6901,6943,7003,7009,7093,7097,7139,7169,7171,7181,7261,7303,7313,7339,7367,7379,7381,7421,7439,7493,7571,7597,7661,7697,7729,7739,7747,7783,7831,7849,7897,7913,7991,8003,8023,8077,8083,8107,8131,8201,8213,8299,8321,8357,8413,8471,8479,8507,8509,8557,8591,8639,8662,8777,8791,8851,8909,8977,9017,9071,9089,9169,9179,9211,9259,9263,9301,9313,9353,9487,9514,9577,9593,9617,9727,9853,9869,9917,9943,9971,9983,10117,10123,10187,10207,10229,10309,10441,10481,10519,10547,10553,10561,10579,10669,10679,10721,10763,10919,10921,11041,11147,11183,11189,11269,11323,11387,11573,11591,11623,11651,11741,11773,11819,11857,11993,11999,12017,12031,12127,12137,12139,12283,12349,12449,12567,12667,12709,12773,12797,12851,12871,12931,12993,13157,13199,13303,13333,13393,13511,13561,13603,13621,13703,13747,13847,13969,13987,14101,14129,14137,14213,14219,14271,14579,14701,14809,14941,14981,15163,15209,15311,15343,15517,15611,15677,15833,15871,15989,16013,16043,16117,16147,16259,16409,16531,16543,16817,16969,17111,17219,17621,17821,18023,18157,18247,18559,18673,18827,18961,19099,19241,19363,19667,19951,20093,20519,20803 1 17 2 19 3 23 4 29 5 31 6 37 7 41 8 43 9 47 10 53 11 59 12 61 13 67 14 71 15 289 16 305 17 323 18 335 19 355 20 361 21 371 22 391 23 413 24 427 25 437 26 469 27 473 28 481 29 493 30 497 31 517 32 527 33 529 34 533 35 551 36 559 37 583 38 589 39 611 40 629 41 649 42 667 43 671 44 689 45 697 46 703 47 713 48 731 49 737 50 767 51 779 52 781 53 793 54 799 55 817 56 841 57 851 58 871 59 893 60 899 61 901 62 923 63 943 64 961 65 989 66 1003 67 1007 68 1037 69 1073 70 1081 71 1121 72 1139 73 1147 74 1159 75 1189 76 1207 77 1219 78 1247 79 1271 80 1273 81 1333 82 1349 83 1357 84 1363 85 1369 86 1387 87 1403 88 1457 89 1501 90 1517 91 1537 92 1541 93 1577 94 1591 95 1633 96 1643 97 1675 98 1679 99 1681 100 1691 101 1711 102 1739 103 1763 104 1769 105 1775 106 1817 107 1829 108 1849 109 1891 110 1909 111 1927 112 1943 113 1961 114 2021 115 2047 116 2059 117 2077 118 2117 119 2173 120 2183 121 2201 122 2209 123 2231 124 2257 125 2263 126 2279 127 2291 128 2323 129 2369 130 2407 131 2419 132 2449 133 2461 134 2479 135 2491 136 2501 137 2537 138 2573 139 2581 140 2623 141 2627 142 2701 143 2747 144 2759 145 2773 146 2809 147 2813 148 2867 149 2881 150 2911 151 2923 152 2929 153 2987 154 2993 155 3007 156 3053 157 3071 158 3103 159 3127 160 3131 161 3139 162 3149 163 3161 164 3193 165 3233 166 3239 167 3277 168 3283 169 3293 170 3317 171 3337 172 3379 173 3397 174 3403 175 3431 176 3479 177 3481 178 3503 179 3551 180 3569 181 3589 182 3599 183 3649 184 3683 185 3713 186 3721 187 3737 188 3763 189 3799 190 3811 191 3827 192 3869 193 3901 194 3937 195 3953 196 3959 197 3973 198 3977 199 4031 200 4033 201 4061 202 4087 203 4141 204 4171 205 4181 206 4183 207 4187 208 4189 209 4223 210 4247 211 4307 212 4309 213 4331 214 4343 215 4387 216 4399 217 4429 218 4453 219 4469 220 4489 221 4559 222 4601 223 4619 224 4633 225 4661 226 4681 227 4687 228 4699 229 4717 230 4747 231 4757 232 4819 233 4841 234 4847 235 4859 236 4891 237 4897 238 5029 239 5041 240 5063 241 5069 242 5123 243 5141 244 5143 245 5183 246 5207 247 5251 248 5293 249 5311 250 5353 251 5371 252 5429 253 5459 254 5461 255 5513 256 5561 257 5587 258 5609 259 5617 260 5633 261 5671 262 5699 263 5723 264 5777 265 5809 266 5891 267 5893 268 5917 269 5959 270 5963 271 5969 272 5977 273 5989 274 6031 275 6077 276 6109 277 6157 278 6161 279 6179 280 6191 281 6283 282 6313 283 6319 284 6401 285 6407 286 6431 287 6437 288 6439 289 6493 290 6499 291 6527 292 6533 293 6623 294 6649 295 6667 296 6683 297 6731 298 6751 299 6767 300 6847 301 6887 302 6893 303 6901 304 6943 305 7003 306 7009 307 7093 308 7097 309 7139 310 7169 311 7171 312 7181 313 7261 314 7303 315 7313 316 7339 317 7367 318 7379 319 7381 320 7421 321 7439 322 7493 323 7571 324 7597 325 7661 326 7697 327 7729 328 7739 329 7747 330 7783 331 7831 332 7849 333 7897 334 7913 335 7991 336 8003 337 8023 338 8077 339 8083 340 8107 341 8131 342 8201 343 8213 344 8299 345 8321 346 8357 347 8413 348 8471 349 8479 350 8507 351 8509 352 8557 353 8591 354 8639 355 8662 356 8777 357 8791 358 8851 359 8909 360 8977 361 9017 362 9071 363 9089 364 9169 365 9179 366 9211 367 9259 368 9263 369 9301 370 9313 371 9353 372 9487 373 9514 374 9577 375 9593 376 9617 377 9727 378 9853 379 9869 380 9917 381 9943 382 9971 383 9983 384 10117 385 10123 386 10187 387 10207 388 10229 389 10309 390 10441 391 10481 392 10519 393 10547 394 10553 395 10561 396 10579 397 10669 398 10679 399 10721 400 10763 401 10919 402 10921 403 11041 404 11147 405 11183 406 11189 407 11269 408 11323 409 11387 410 11573 411 11591 412 11623 413 11651 414 11741 415 11773 416 11819 417 11857 418 11993 419 11999 420 12017 421 12031 422 12127 423 12137 424 12139 425 12283 426 12349 427 12449 428 12567 429 12667 430 12709 431 12773 432 12797 433 12851 434 12871 435 12931 436 12993 437 13157 438 13199 439 13303 440 13333 441 13393 442 13511 443 13561 444 13603 445 13621 446 13703 447 13747 448 13847 449 13969 450 13987 451 14101 452 14129 453 14137 454 14213 455 14219 456 14271 457 14579 458 14701 459 14809 460 14941 461 14981 462 15163 463 15209 464 15311 465 15343 466 15517 467 15611 468 15677 469 15833 470 15871 471 15989 472 16013 473 16043 474 16117 475 16147 476 16259 477 16409 478 16531 479 16543 480 16817 481 16969 482 17111 483 17219 484 17621 485 17821 486 18023 487 18157 488 18247 489 18559 490 18673 491 18827 492 18961 493 19099 494 19241 495 19363 496 19667 497 19951 498 20093 499 20519 500 20803 Primes contained in the terms 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 ============================================================= 17 17 19 19 23 23 29 29 31 31 37 37 41 41 43 43 47 47 53 53 59 59 61 61 67 67 71 71 289 17 305 5 61 323 17 19 335 5 67 355 5 71 361 19 371 7 53 391 17 23 413 7 59 427 7 61 437 19 23 469 7 67 473 11 43 481 13 37 493 17 29 497 7 71 517 11 47 527 17 31 529 23 533 13 41 551 19 29 559 13 43 583 11 53 589 19 31 611 13 47 629 17 37 649 11 59 667 23 29 671 11 61 689 13 53 697 17 41 703 19 37 713 23 31 731 17 43 737 11 67 767 13 59 779 19 41 781 11 71 793 13 61 799 17 47 817 19 43 841 29 851 23 37 871 13 67 893 19 47 899 29 31 901 17 53 923 13 71 943 23 41 961 31 989 23 43 1003 17 59 1007 19 53 1037 17 61 1073 29 37 1081 23 47 1121 19 59 1139 17 67 1147 31 37 1159 19 61 1189 29 41 1207 17 71 1219 23 53 1247 29 43 1271 31 41 1273 19 67 1333 31 43 1349 19 71 1357 23 59 1363 29 47 1369 37 1387 19 (73) 1403 23 61 1457 31 47 1501 19 (79) 1517 37 41 1537 29 53 1541 23 67 1577 19 (83) 1591 37 43 1633 23 71 1643 31 53 1675 5 67 1679 23 (73) 1681 41 1691 19 (89) 1711 29 59 1739 37 47 1763 41 43 1769 29 61 1775 5 71 1817 23 (79) 1829 31 59 1849 43 1891 31 61 1909 23 (83) 1927 41 47 1943 29 67 1961 37 53 2021 43 47 2047 23 (89) 2059 29 71 2077 31 67 2117 29 (73) 2173 41 53 2183 37 59 2201 31 71 2209 47 2231 23 (97) 2257 37 61 2263 31 (73) 2279 43 53 2291 29 (79) 2323 23 (101) 2369 23 (103) 2407 29 (83) 2419 41 59 2449 31 (79) 2461 23 (107) 2479 37 67 2491 47 53 2501 41 61 2537 43 59 2573 31 (83) 2581 29 (89) 2623 43 61 2627 37 71 2701 37 (73) 2747 41 67 2759 31 (89) 2773 47 59 2809 53 2813 29 (97) 2867 47 61 2881 43 67 2911 41 71 2923 37 (79) 2929 29 (101) 2987 29 (103) 2993 41 (73) 3007 31 (97) 3053 43 71 3071 37 (83) 3103 29 (107) 3127 53 59 3131 31 (101) 3139 43 (73) 3149 47 67 3161 29 (109) 3193 31 (103) 3233 53 61 3239 41 (79) 3277 29 (113) 3283 7 67 3293 37 (89) 3317 31 (107) 3337 47 71 3379 31 (109) 3397 43 (79) 3403 41 (83) 3431 47 (73) 3479 7 71 3481 59 3503 31 (113) 3551 53 67 3569 43 (83) 3589 37 (97) 3599 59 61 3649 41 (89) 3683 29 (127) 3713 47 (79) 3721 61 3737 37 (101) 3763 53 71 3799 29 (131) 3811 37 (103) 3827 43 (89) 3869 53 (73) 3901 47 (83) 3937 31 (127) 3953 59 67 3959 37 (107) 3973 29 (137) 3977 41 (97) 4031 29 (139) 4033 37 (109) 4061 31 (131) 4087 61 67 4141 41 (101) 4171 43 (97) 4181 37 (113) 4183 47 (89) 4187 53 (79) 4189 59 71 4223 41 (103) 4247 31 (137) 4307 59 (73) 4309 31 (139) 4331 61 71 4343 43 (101) 4387 41 (107) 4399 53 (83) 4429 43 (103) 4453 61 (73) 4469 41 (109) 4489 67 4559 47 (97) 4601 43 (107) 4619 31 (149) 4633 41 (113) 4661 59 (79) 4681 31 (151) 4687 43 (109) 4699 37 (127) 4717 53 (89) 4747 47 (101) 4757 67 71 4819 61 (79) 4841 47 (103) 4847 37 (131) 4859 43 (113) 4891 67 (73) 4897 59 (83) 5029 47 (107) 5041 71 5063 61 (83) 5069 37 (137) 5123 47 (109) 5141 53 (97) 5143 37 (139) 5183 71 (73) 5207 41 (127) 5251 59 (89) 5293 67 (79) 5311 47 (113) 5353 53 (101) 5371 41 (131) 5429 61 (89) 5459 53 (103) 5461 43 (127) 5513 37 (149) 5561 67 (83) 5587 37 (151) 5609 71 (79) 5617 41 (137) 5633 43 (131) 5671 53 (107) 5699 41 (139) 5723 59 (97) 5777 53 (109) 5809 37 (157) 5891 43 (137) 5893 71 (83) 5917 61 (97) 5959 59 (101) 5963 67 (89) 5969 47 (127) 5977 43 (139) 5989 53 (113) 6031 37 (163) 6077 59 (103) 6109 41 (149) 6157 47 (131) 6161 61 (101) 6179 37 (167) 6191 41 (151) 6283 61 (103) 6313 59 (107) 6319 71 (89) 6401 37 (173) 6407 43 (149) 6431 59 (109) 6437 41 (157) 6439 47 (137) 6493 43 (151) 6499 67 (97) 6527 61 (107) 6533 47 (139) 6623 37 (179) 6649 61 (109) 6667 59 (113) 6683 41 (163) 6731 53 (127) 6751 43 (157) 6767 67 (101) 6847 41 (167) 6887 71 (97) 6893 61 (113) 6901 67 (103) 6943 53 (131) 7003 47 (149) 7009 43 (163) 7093 41 (173) 7097 47 (151) 7139 11 59 7169 67 (107) 7171 71 (101) 7181 43 (167) 7261 53 (137) 7303 67 (109) 7313 71 (103) 7339 41 (179) 7367 53 (139) 7379 47 (157) 7381 11 61 7421 41 (181) 7439 43 (173) 7493 59 (127) 7571 67 (113) 7597 71 (107) 7661 47 (163) 7697 43 (179) 7729 59 (131) 7739 71 (109) 7747 61 (127) 7783 43 (181) 7831 41 (191) 7849 47 (167) 7897 53 (149) 7913 41 (193) 7991 61 (131) 8003 53 (151) 8023 71 (113) 8077 41 (197) 8083 59 (137) 8107 11 67 8131 47 (173) 8201 59 (139) 8213 43 (191) 8299 43 (193) 8321 53 (157) 8357 61 (137) 8413 47 (179) 8471 43 (197) 8479 61 (139) 8507 47 (181) 8509 67 (127) 8557 43 (199) 8591 11 71 8639 53 (163) 8662 2 61 71 8777 67 (131) 8791 59 (149) 8851 53 (167) 8909 59 (151) 8977 47 (191) 9017 71 (127) 9071 47 (193) 9089 61 (149) 9169 53 (173) 9179 67 (137) 9211 61 (151) 9259 47 (197) 9263 59 (157) 9301 71 (131) 9313 67 (139) 9353 47 (199) 9487 53 (179) 9514 2 67 71 9577 61 (157) 9593 53 (181) 9617 59 (163) 9727 71 (137) 9853 59 (167) 9869 71 (139) 9917 47 (211) 9943 61 (163) 9971 13 59 9983 67 (149) 10117 67 (151) 10123 53 (191) 10187 61 (167) 10207 59 (173) 10229 53 (193) 10309 13 61 10441 53 (197) 10481 47 (223) 10519 67 (157) 10547 53 (199) 10553 61 (173) 10561 59 (179) 10579 71 (149) 10669 47 (227) 10679 59 (181) 10721 71 (151) 10763 47 (229) 10919 61 (179) 10921 67 (163) 11041 61 (181) 11147 71 (157) 11183 53 (211) 11189 67 (167) 11269 59 (191) 11323 13 67 11387 59 (193) 11573 71 (163) 11591 67 (173) 11623 59 (197) 11651 61 (191) 11741 59 (199) 11773 61 (193) 11819 53 (223) 11857 71 (167) 11993 67 (179) 11999 13 71 12017 61 (197) 12031 53 (227) 12127 67 (181) 12137 53 (229) 12139 61 (199) 12283 71 (173) 12349 53 (233) 12449 59 (211) 12567 3 59 71 12667 53 (239) 12709 71 (179) 12773 53 (241) 12797 67 (191) 12851 71 (181) 12871 61 (211) 12931 67 (193) 12993 3 61 71 13157 59 (223) 13199 67 (197) 13303 53 (251) 13333 67 (199) 13393 59 (227) 13511 59 (229) 13561 71 (191) 13603 61 (223) 13621 53 (257) 13703 71 (193) 13747 59 (233) 13847 61 (227) 13969 61 (229) 13987 71 (197) 14101 59 (239) 14129 71 (199) 14137 67 (211) 14213 61 (233) 14219 59 (241) 14271 3 67 71 14579 61 (239) 14701 61 (241) 14809 59 (251) 14941 67 (223) 14981 71 (211) 15163 59 (257) 15209 67 (227) 15311 61 (251) 15343 67 (229) 15517 59 (263) 15611 67 (233) 15677 61 (257) 15833 71 (223) 15871 59 (269) 15989 59 (271) 16013 67 (239) 16043 61 (263) 16117 71 (227) 16147 67 (241) 16259 71 (229) 16409 61 (269) 16531 61 (271) 16543 71 (233) 16817 67 (251) 16969 71 (239) 17111 71 (241) 17219 67 (257) 17621 67 (263) 17821 71 (251) 18023 67 (269) 18157 67 (271) 18247 71 (257) 18559 67 (277) 18673 71 (263) 18827 67 (281) 18961 67 (283) 19099 71 (269) 19241 71 (271) 19363 17 67 19667 71 (277) 19951 71 (281) 20093 71 (283) 20519 17 71 20803 71 (293)