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Index to OEIS: Section Pri

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Index to OEIS: Section Pri

[ Aa | Ab | Al | Am | Ap | Ar | Ba | Be | Bi | Bl | Bo | Br | Ca | Ce | Ch | Cl | Coa | Coi | Com | Con | Cor | Cu | Cy | Da | De | Di | Do | Ea | Ed | El | Eu | Fa | Fe | Fi | Fo | Fu | Ga | Ge | Go | Gra | Gre | Ha | He | Ho | Ia | In | J | K | La | Lc | Li | Lo | Lu | M | Mag | Map | Mat | Me | Mo | Mu | N | Na | Ne | Ni | No | Nu | O | Pac | Par | Pas | Pea | Per | Ph | Poi | Pol | Pos | Pow | Pra | Pri | Pro | Ps | Qua | Que | Ra | Rea | Rel | Res | Ro | Ru | Sa | Se | Si | Sk | So | Sp | Sq | St | Su | Sw | Ta | Te | Th | To | Tra | Tri | Tu | U | V | Wa | We | Wi | X | Y | Z | 1 | 2 | 3 | 4 ]

prime divisor, greatest: A006530
prime factorizations of important sequences: see factorizations of important sequences

prime factors, sequences related to:

prime factors: at least 1: A000027 2: A002808 3: A033942 4: A033987 5: A046304,
6: A046305 7: A046307 8: A046309 9: A046311 10: A046313
prime factors: at most 1: A000040 2: A037143 3: A037144 4: A166718 5: A166719
prime factors: exactly 1: A000040 2: A001358 3: A014612 4: A014613 5: A014614
6: A046306 7: A046308 8: A046310 9: A046312 10: A046314 11: A069272 12: A069273 13: A069274 14: A069275 15: A069276 16: A069277 17: A069278 18: A069279 19: A069280 20: A069281
prime factors: number of A001222 (with multiplicity), A001221 (distinct)
prime factors: see also distinct prime factors
prime factors: table of: A078840
prime factors in a given set:
(we list the set of numbers, then the set in which they have their prime factors)
Finite subsets: (see also perfect powers
A003586 (3-smooth: {2,3}), A051037 (5-smooth: {2,3,5}), A002473 (7-smooth: {2,3,5,7}), A051038 (11-smooth: {2,3,5,7,11}), A080197 (13-smooth: {2,3,5,7,11,13}),
A080681 (17-smooth: {2,3,5,7,11,13,17}), A080682 (19-smooth: {2,3,5,7,11,13,17,19}), A080683 (23-smooth: {2,3,5,7,11,13,17,19,23}).
A003591 ({2,7}), A003592 ({2,5}), A003593 (odd 5-smooth: {3,5}), A003594 ({3,7}), A003595 ({5,7}), A003596 ({2,11}), A003597 ({3,11}), A003598 ({5,11}), A003599 ({7,11}).
congruence related: A000079 (even: powers of 2) A005408 (odd primes: A005408),
A004613 (primes p==1 mod 4: A004613), A004614 (p==3 mod 4: A004614), A004611 (p==1 mod 6: A004611), A004612 (factors p==5 mod 6: A004612)
digit related: A004022 (prime factors having only digit 1: A004022) A020449 (primes with only digit 0 & 1: A020449),
A036302 (only digit 1 & 2: A036302), A036303 (only digit 1 & 3: A036303), A036304 (only digit 1 & 4: A036304), A036305 (only digit 1 & 5: A036305), A036306 (only digit 1 & 6: A036306),
A036307 (only digit 1 & 7: A036307), A036308 (only digit 1 & 8: A036308), A036309 (only digit 1 & 9: A036309), A036310 (only digit 2 & 3: A036310), A036311 (only digit 2 & 5: A036311),
A036312 (only digit 2 & 7: A036312), A036313 (only digit 2 & 9: A036313), A036314 (only digit 3 & 4: A036314), A036315 (only digit 3 & 5: A036315), A036316 (only digit 3 & 7: A036316),
A036317 (only digit 3 & 8: A036317), A036318 (only digit 4 & 7: A036318), A036319 (only digit 4 & 9: A036319), A036320 (only digit 5 & 7: A036320), A036321 (only digit 5 & 9: A036321),
A036322 (only digit 6 & 7: A036322), A036323 (only digit 7 & 8: A036323), A036324 (only digit 7 & 9: A036324), A036325 (only digit 8 & 9: A036325).

prime index: (index of the n-th prime): A000720

prime indices, sequences computed from:

prime indices, sequences computed from, bijections (1): A122111, A153212, A241909, A241916, A242415
prime indices, sequences computed from, bijections (2): A242419, A069799, A105119, A225891, A242420
prime indices, sequences computed from, Bulgarian solitaire operation: A242424
prime indices, sequences computed from, difference between the largest and the smallest index: A243055
prime indices, sequences computed from, difference between the two largest indices: A242411
prime indices, sequences computed from, max: A061395
prime indices, sequences computed from, min: A055396
prime indices, sequences computed from, product of indices (with multiplicity): A003963
prime indices, sequences computed from, shift binary trees: A005940, A163511, A253563, A253565
prime indices, sequences computed from, shift dispersion arrays: A246278 (A246279)
prime indices, sequences computed from, shift operations: A003961, A064989, A253550
prime indices, sequences computed from, sum of differences between all index pairs: A261079
prime indices, sequences computed from, sum of indices (with multiplicity): A056239
prime indices, sequences computed from, Sum sign(i) over all indices i, with multiplicity, i.e., number of prime divisors: A001222
prime indices, sequences computed from: see also Matula-Goebel numbers

prime numbers of measurement: A002048*, A002049*
prime numbers: A000040*, A008578
prime plus twice a square: A046903

prime powers, sequences related to:

prime powers: base: A025473, exponent: A025474
prime powers: complement of: A024619
prime powers: differences: A036689 (p^2-p), A127917 (p^3-p), A135177 (p^3-p^2), A138401 (p^4-p), A138402 (p^4-p^2), A138403 (p^4-p^3), A138404 (p^5-p), A138405 (p^5-p^2), A138406 (p^5-p^3), A138407 (p^5-p^4), A138408 (p^6-p), A138409 (p^6-p^2), A138410 (p^6-p^3), A138411 (p^6-p^4)
prime powers: excluding primes: base: A025476, exponent: A025477
prime powers: excluding primes: complement of: A085971
prime powers: excluding primes: gaps: A053707
prime powers: excluding primes: gaps: record: A167186, start: A167188, end: A167189
prime powers: excluding primes: list of: A025475, previous: A167185, next: A167184
prime powers: excluding primes: number of: A085501
prime powers: gaps: A057820
prime powers: gaps: record: A121492, start: A002540, end: A167236
prime powers: list of: A000961, previous: A031218, next: A000015
prime powers: number of: A065515

prime pyramid: A051237*, A036440
prime quadruples: A007530

prime races, sequences related to:

prime races: A007350, A007351, A007352, A007353, A007354, A007355, A096447, A096448, A096449, A096450, A096451, A096452, A096453, A096454, A096455, A098044
prime races: see also races

prime signature, sequences related to:

prime signature: A025487*
prime signature omega=1: A000040 [1], A001248 [2], A030078 [3], A030514 [4], A050997 [5], A030516 [6], A092759 [7], A179645 [8], A179665 [9], A030629 [10], A079395 [11], A030631 [12], A138031 [13]
prime signature omega=2: A006881 [1,1], A054753 [1,2], A065036 [1,3], A085986 [2,2], A178739 [1,4], A143610 [2,3], A178740 [1,5], A189988 [2,4], A162142 [3,3], A179666 [3,4], A179646 [2,5], A189987 [1,6], A189991 [4,4], A179671 [3,5], A189990 [2,6], A179664 [1,7]
prime signature omega=3: A007304 [1,1,1], A085987 [1,1,2], A189975 [1,1,3], A179643 [1,2,2], A179644 [1,1,4], A163569 [1,2,3], A162143 [2,2,2], A179669 [1,2,4], A179667 [1,1,5], A179695 [2,2,3], A179688 [1,3,3], A190106 [2,3,3], A179746 [2,2,4], A179698 [1,3,4], A179691 [1,2,5], A179672 [1,1,6]
prime signature omega=4: A046386 [1,1,1,1], A189982 [1,1,1,2], A179690 [1,1,2,2], A179670 [1,1,1,3], A189344 [1,2,2,2], A179700 [1,1,2,3], A179693 [1,1,1,4], A190377 [2,2,2,2], A190109 [1,2,2,3], A190108 [1,1,3,3], A190107 [1,1,2,4], A179704 [1,1,1,5]
prime signature omega=5: A046387 [1,1,1,1,1], A189983 [1,1,1,1,2], A189989 [1,1,1,2,2], A189984 [1,1,1,1,3], A190379 [1,1,2,2,2], A190111 [1,1,1,2,3], A190110 [1,1,1,1,4]
prime signature omega=6: A067885 [1,1,1,1,1,1], A189985 [1,1,1,1,1,2], A190380 [1,1,1,1,2,2], A190378 [1,1,1,1,1,3]
prime signature omega=7: A123321 [1,1,1,1,1,1,1], A190381 [1,1,1,1,1,1,2]
prime signature omega=8: A123322 [1,1,1,1,1,1,1,1]
prime signature: see also (1) A000688 A005361 A008480 A008683 A008966 A025488 A035206 A035341 A036035 A036041 A038538 A046523 A046660
prime signature: see also (2) A046951 A050320 A050322 A050323 A050324 A050325 A050326 A050327 A050328 A050329 A050330 A050331
prime signature: see also (3) A050332 A050333 A050334 A050335 A050336 A050337 A050338 A050339 A050340 A050341 A050345 A050346
prime signature: see also (4) A050347 A050348 A050349 A050350 A050354 A050355 A050356 A050357 A050358 A050359 A050360 A050361
prime signature: see also (5) A050362 A050363 A050364 A050370 A050371 A050372 A050373 A050374 A050375 A050377 A050378 A050379
prime signature: see also (6) A050380 A050382 A051282 A051466 A051707 A052213 A052214 A052304 A052305 A052306 A056099 A056153
prime signature: see also (7) A056808 A056823 A057335 A343511
prime signature: see also (8) exponents in factorization, sequences computed from
prime signature: see also (9) primes, in arithmetic progressions
prime signature: subsequences of A025487:

prime triples: A007529
prime(2^n): A033844*, A018249, A051438, A051440, A051439
prime(k^n): A033844, A038833, A119772, A055680, A058192, A058239, A119773, A119774, A006988, A058244, A058245, A058246, A119775, A119776, A119777
prime(n) == +-k (mod n): (1) A023143, A023144, A023145, A023146, A023147, A023148, A023149, A023150, A023151, A023152, A049204, A092044
prime(n) == +-k (mod n): (2) A092045, A092046, A092047, A092048, A092049, A092050, A092051, A092052
prime, largest <=n: A007917
prime, largest dividing n: A006530
prime, smallest whose product of digits is (something): A088653 A088654 A089298 A089364 A089365 A089386 A089912
prime, weakly: A050249
PRIMEGAME: A007542, A007546, A007547
PrimePi(x), number of primes <= x: A000720*

primes, sequences related to:

primes: A000040*
primes gaps, see primes, gaps between
primes in Lucas U-sequences: A049883 U(1,-2), A005478 U(1,-1), A086383 U(2,-1), A000040 U(2,1), A201000 U(3,-2), A201001 U(3,-1), A000668 U(3,2), A076481 U(4,3), A201002 U(5,-2), A201005 U(5,-1)
primes in arithmetic progressions, see primes, in arithmetic progressions
primes involving quasi-repdigits D(R)nE: (01) A049054, A088274, A088275, A102929, A102930, A102931, A102932, A102933, A102934, A102935,
primes involving quasi-repdigits D(R)nE: (02) A102936, A102937, A102938, A102939, A102940, A102941, A102942, A102943, A102944, A102945,
primes involving quasi-repdigits D(R)nE: (03) A102946, A102947, A081677, A101392, A102948, A102949, A102950, A102951, A102952, A102953,
primes involving quasi-repdigits D(R)nE: (04) A102954, A102955, A098930, A099006, A102956, A098959, A102957, A098960, A102958, A102959,
primes involving quasi-repdigits D(R)nE: (05) A102959, A102960, A102961, A102962, A102963, A102964, A056807, A100501, A101393, A102965,
primes involving quasi-repdigits D(R)nE: (06) A102966, A102967, A102968, A102969, A102970, A102971, A102972, A102973, A102974, A102975,
primes involving quasi-repdigits D(R)nE: (07) A102976, A102977, A102978, A102979, A102980, A101396, A101398, A056806, A101397, A101395,
primes involving quasi-repdigits D(R)nE: (08) A101394, A102981, A102982, A102983, A102984, A102985, A102986, A102987, A102988, A102989,
primes involving quasi-repdigits D(R)nE: (09) A102990, A102991, A102992, A102993, A102994, A099005, A099017, A102995, A102996, A102997,
primes involving quasi-repdigits D(R)nE: (10) A102998, A102999, A103000, A103001, A103002, A103003, A096254, A103004, A103005, A103006,
primes involving quasi-repdigits D(R)nE: (11) A103007, A103008, A103009, A103010, A103011, A103012, A103013, A103014, A103015, A103016,
primes involving quasi-repdigits D(R)nE: (12) A103017,A103018,A103019,A103020,A103021,A103022,A103023,A103024,A103025,A056805,
primes involving quasi-repdigits D(R)nE: (13) A103027,A103027,A103028,A103029,A103030,A097402,A103031,A103032,A103033,A103034,
primes involving quasi-repdigits D(R)nE: (14) A103035,A103036,A103037,A103038,A103039,A103040,A103041,A103042,A103043,A103044,
primes involving quasi-repdigits D(R)nE: (15) A103045,A103046,A103047,A103048,A103049,A056804,A097970,A097954,A103050,A103051,
primes involving quasi-repdigits D(R)nE: (16) A103052,A103053,A103054,A103055,A103056,A103057,A103058,A103059,A103060,A103061,
primes involving quasi-repdigits D(R)nE: (17) A103062,A103063,A103064,A103065,A103066,A103067,A103068,A099190,A103069,A103070,
primes involving quasi-repdigits D(R)nE: (18) A103071,A103072,A103073,A103074,A103075,A103076,A103077,A103078,A103079,A103080,
primes involving quasi-repdigits D(R)nE: (19) A103081,A103082,A103083,A103084,A103085,A103086,A103087,A103088,A103089,A103090,
primes involving quasi-repdigits D(R)nE: (20) A103091,A103092,A056797,A096774,A100473,A103093,A103094,A103095,A103096,A103097,
primes involving quasi-repdigits D(R)nE: (21) A103098,A103099,A103100,A103101,A103102,A103103,A103104,A103105,A103106,A103107,
primes involving quasi-repdigits D(R)nE: (22) A103108,A103109
primes, decimal representation of, sequences related to:
numbers which yield primes when digits/strings are inserted / prefixed / appended:
A164329 (prime when 0 is inserted anywhere), A216169 (subset of composite terms), A215417 (subset of primes), A159236 (0 is inserted between all digits).
A068673 (1 is prefixed, or appended), A304246 (1 is inserted anywhere), A068679 (1 is prefixed, appended or inserted), A069246 (primes among these).
A304247 (2 is inserted anywhere).
A304248 (3 is inserted anywhere), A068674 (3 is prefixed or appended), A158594 (3 is prefixed, appended or inserted anywhere), A215419 (primes among these).
A068677 (7 is prefixed or appended), A069832 (7 is prefixed, appended or inserted anywhere), A215420 (primes among these).
A069833 (9 is prefixed, appended or inserted anywhere), A215421 (primes among these).
A158232 (13 is prefixed or appended).
A304243 (2 is prefixed or prime(k+2) is inserted after the k-th digit), A304244 (prime(k) is inserted after the k-th digit), A304245 (2 is inserted after the first, or prime(k+1) after the k-th digit, k > 1).
primes with digits in a given set:
primes with only the digit '1': A004022
primes with digits in {0,1}: A020449, {1,2}: A020450, ..., A020457 (1,9), ..., A020469 (6,7), A020470 (7,8), A020471 (7,9), A020472 (8,9).
primes with digits in {...}: A036953 (0,1,2), A260044 (0,1,3), A260266 (0,1,4), A199325 (0,1,5) - A199329 (0,1,9), A061247 (0,1,8);
primes with digits in {...}: A260267 (1,2,4), A260268 (1,4,5) - A260271 (1,4,9); A199340 (0,3,4) - A199349 (3,4,9). (To be completed.)

primes involving decimal expansion of n:

A018800, A030665, A062584, A068164, A068695*, A069691, A077344, A077345, A077501, A084413, A084414, A088781, A090287, A091088, A091089, A228323, A228324, A228325, A258190, A258337, A262369, A338366, A337834, A338715, A338716
Base 2 versions: A164022, A262365, A262366
See also A030000, A032352, A032734, A082058
primes involving repunits, sequences related to:
near-repdigit primes: A164937
-, having X = 2, ..., 9 as repeated digit: A105982 (2), A105981 (3), A105980 (4), A105979 (5), A105978 (6), A105977 (7), A105976 (8), A105975 (9).
near-repunit primes: A105992, A034093 (number of primes by changing one 1 to 0), A065083 (least k for which A034093(k) = n).
-, that contain the digit X: A065074 (0), ...
primes involving repunits, X*repunit*10+Y (i.e., of form X...XY, A-numbers are labelled (X,Y) below):
A004023 (1,1), A056654 (1,3), A056655 (1,7), A056659 (1,9), A056660 (2,1), A056656 (2,3), A056677 (2,7), A056678 (2,9), A055520 (3,1),
A056680 (3,7), A056681 (4,1), A056661 (4,3), A056682 (4,7), A056683 (4,9), A056684 (5,1), A056685 (5,3), A056686 (5,7), A056687 (5,9),
A056658 (6,1), A056657 (6,7), A056688 (7,1), A056689 (7,3), A056693 (7,9), A056664 (8,1), A056694 (8,3), A056695 (8,7), A056663 (8,9),
A056696 (9,1), A056662 (9,7).
primes involving repunits, X*10^n+Y*repunit (i.e., of form XY...Y, A-numbers are labelled (X,Y) below):
A004023 (1,1), A056698 (1,3), A089147 (1,7), A002957 (1,9), A056700 (2,1), A056701 (2,3), A056702 (2,7), A056703 (2,9), A056704 (3,1),
A056705 (3,7), A056706 (4,1), A056707 (4,3), A056708 (4,7), A056712 (4,9), A056713 (5,1), A056714 (5,3), A056715 (5,7), A056716 (5,9),
A056717 (6,1), A056718 (6,7), A056719 (7,1), A056720 (7,3), A056721 (7,9), A056722 (8,1), A056723 (8,3), A056724 (8,7), A056725 (8,9),
A056726 (9,1), A056727 (9,7).
primes involving repunits, X*repunit +- Y (= X*repunit*10 +- Y-X, cf. above):
A004023 (1...1), A097683 (1..13), A097684 (1..17), A097685 (1..19), A084832 (2..21), A096506 (2..23), A099409 (2..27),
A099410 (2..29), A055557 (3..31), A099411 (3..37), A099412 (4..41), A096845 (4..43), A099413 (4..47), A099414 (4..49),
A099415 (5..51), A099416 (5..53), A099417 (5..57), A099418 (5..59), A098088 (6..61), A096507 (6..67), A099419 (7..71),
A099420 (7..73), A098089 (7..79), A099421 (8..81), A099422 (8..83), A096846 (8..87), A096508 (8..89), A095714 (9..91), A089675 (9..97).
primes involving repunits, X*repunit(2n+1) +- (Y-+X)*10^n (= X..XYX..X = near-repdigit palindromic primes):
A331862 (1,0), A004023 (1...1), A331865 (1,2), A077779 = A107123*2+1 & A331865 (1,3), A077780 = A107124*2+1 & A331866 (1,4), A077783 = A107125*2+1 (1,5), A077787 = A107126*2+1 (1,6), A077789 = A107127*2+1 (1,7), A077791 = A107648*2+1 (1,8), A077795 = A107649*2+1 (1,9),
A077775 = A183174*2+1 (3,1), A077784 = A183175*2+1 (3,5), A077790 = A183176*2+1 (3,7), A077792 = A183177*2+1 (3,8),
A077777 = A183178*2+1 (7,2), A077781 = A183179*2+1 (7,4), A077785 (7,5), A077788 = 2*A183181 + 1 (7,6), A077793 = A183182*2+1 (7,8), A077796 = 2*A183183 + 1 (7,9),
A077776 = A183184*2+1 (9,1), A077778 = A115073*2+1 (9,2), A077782 = A183185*2+1 (9,4), A077786 = A183186*2+1 (9,5), A077794 = 2*A183187(n)+1 (9,8).
repunit primes: A004022, A004023 (indices of primes in repunits A002275).

primes of the form binomial(k*n, n) +- 1, k=2..6: A066699, A066726, A125221, A125220, A125241, A125240, A125243, A125242, A125245, A125244
primes p such that x^k = 2 has a solution mod p, sequences related to:
primes p such that x^k = 2 has a solution mod p, (**) means the divergence occurs beyond the last entry shown in the OEIS.
primes p such that x^k = 2 has a solution mod p, k=1 to 9: A000040, A038873 (or A001132), A040028, A040098, A040159, A040992, A042966, A045315(**), A049596,
primes p such that x^k = 2 has a solution mod p, k=10 to 20: A049542, A049543, A049544, A049545, A049546, A049547, A045315, A049549, A049550, A049551
primes p such that x^k = 2 has a solution mod p, k=20 to 29: A049552, A049553, A049554, A049555, A049556, A049557, A049558, A049596(**), A049560, A049561
primes p such that x^k = 2 has a solution mod p, k=30 to 39: A049562, A216883, A049564, A049565, A049566, A049567, A049568, A049569, A049570, A049571
primes p such that x^k = 2 has a solution mod p, k=40 to 49: A049572, A049573, A049574, A058853, A049576, A049577, A049578, A216885, A049580, A042966(**)
primes p such that x^k = 2 has a solution mod p, k=50 to 59: A049582, A049583, A049584, A049585, A049550(**), A049587, A049588, A049589, A049590, A216886
primes p such that x^k = 2 has a solution mod p, k=60 to 63 and 67: A049592, A216884 A049594, A049595, A216887
primes such that the sum of the predecessor and successor primes is divisible by k: A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158
primes that become a different prime under some mapping
see also: primes, sequences related to decimal representation of, digits, maps acting on (to be created).
primes that become a different prime under some mapping (1): A180533 A180535 A180537 A180560 A180541 A180543 A180552 A180581 A180561 A180530 A180526 A180527
primes that become a different prime under some mapping (2): A180545 A180525 A180528 A180531 A180559 A180529 A180532 A180538 A180534 A180517 A180540 A180542
primes that become a different prime under some mapping (3): A180518 A180548 A180547 A180519 A180546 A180549 A180550 A180553 A180520 A180555 A180557 A180521
primes that become a different prime under some mapping (4): A180558 A180522 A180523 A180524 A180536 A180539 A180544 A180554 A180551 A180556
primes whose base-b1 representation also is the base-b2 representation of a prime:
Primes in two bases (1): A235266*, A152079, A235475, A235476, A235477, A235478, A235479, A065720, A235265, A235473, A231474
Primes in two bases (2): A231476, A231477, A231478, A235480, A065721, A235461, A235467, A235474, A235624, A235634, A235633
Primes in two bases (3): A235481, A065722, A235462, A235468, A235615, A235625, A235635, A235632, A235482, A065723, A235463
Primes in two bases (4): A235469, A235616, A235626, A235636, A235631, A231481, A065724 A235464, A235470, A235617, A235627
Primes in two bases (5): A235637, A235630, A231479, A065725, A235465, A235471, A235618, A235628, A235638, A235622, A231480
Primes in two bases (5): A065726, A235466, A235472, A235619, A235629, A235639, A235621, A235620, A065727, A089971, A089981
Primes in two bases (6): A090707, A090708, A090709, A090710, A235394, A235395, A091924, A113016, A235110, A103144
primes with given smallest positive primitive root
primes with X as smallest positive primitive root: (1) A001122, A001123, A001124, A001125, A001126, A061323, A061324, A061325, A061326, A061327,
primes with X as smallest positive primitive root: (2) A061328, A061329, A061330, A061331, A061332, A061333, A061334, A061335, A061730, A061731,
primes with X as smallest positive primitive root: (3) A061732, A061733, A061734, A061735, A061736, A061737, A061738, A061739, A061740, A061741,
primes with X as smallest positive primitive root: (4) A114657, A114658, A114659, A114660, A114661, A114662, A114663, A114664, A114665, A114666,
primes with X as smallest positive primitive root: (5) A114667, A114668, A114669, A114670, A114671, A114672, A114673, A114674, A114675, A114676,
primes with X as smallest positive primitive root: (6) A114677, A114678, A114679, A114680, A114681, A114682, A114683, A114684, A114685, A114686
primes, <= n: A000720*
primes, absolute: A003459*
primes, additive: A046704
primes, almost: see almost primes
primes, approximations to: A050503, A050502, A050504
primes, arithmetic progressions of, see primes, in arithmetic progressions
primes, automorphic: A046883, A046884
primes, balanced: (index) A096693, A096705, A096706, A096707, A096708, A096697, A096709, A096695
primes, balanced: (order) A006562, A082077, A082078, A082079, A096697, A096698, A096699, A096700, A096701, A096702,
primes, balanced: (order) A096703, A096704, A081415, A082080, A126554, A096692, A127557, A096696, A160920, A090403
primes, balanced: (order) A126556, A126558, A126555, A126557, A127364, A126559, A051795, A054342, A090403, A055206
primes, balanced: A006562, A051795, A054342
primes, Bertrand: A006992*, A051501
primes, Bertrand: see also Bertrand's Postulate
Primes, by class number, A002148, A002142, A002146, A002147, A002149
primes, by Erdos-Selfridge class n+: (0) A005113, A126433, A101253
primes, by Erdos-Selfridge class n-: (0) A056637, A101231, A126805
primes, by Erdos-Selfrigde class n+: (1) A005105, A005106, A005107, A005108, A081633, A081634
primes, by Erdos-Selfrigde class n+: (2) A081635, A081636, A081637, A081638, A081639, A084071, A090468, A129474, A129475
primes, by Erdos-Selfrigde class n-: (1) A005109, A005110, A005111, A005112, A081424, A081425
primes, by Erdos-Selfrigde class n-: (2) A081426, A081427, A081428, A081429, A081430, A081640, A081641, A129248, A129249, A129250
Primes, by number of digits, A003617, A006879, A006880, A003618
primes, by order: (1) A007821, A049078, A049079, A049080, A049081, A058322, A058324, A058325, A058326, A058327, A058328, A093046
primes, by order: (2) A000040, A006450, A038580, A049090, A049203, A049202, A057849, A057850, A057851, A057847, A058332, A093047
Primes, by period length, A007615
primes, by primitive root, sequences related to:
Note that for sequences A019334-A019421, which list primes with primitive root m in the range 3 to 99, in order to include primes less than m, we use the essentially equivalent definition "Primes p such that the multiplicative order of m mod p is p-1".
primes having smallest primitive root 2: A001122, 3: A001123, 5: A001124, 6: A001125, 7: A001126.
related: A002230 (least primitive root sets a new record), A003147 (primitive root is a Fibonacci number)
having primitive root 3: A019334, 5: A019335, 6: A019336, 7: A019337, 8: A019338, 10: A001913, -10: A007348, 10 and -10: A007349
11: A019339, 12: A019340, 13: A019341, 14: A019342, 15: A019343, 17: A019344, 18: A019345, 19: A019346, 20: A019347
21: A019348, 22: A019349, 23: A019350, 24: A019351, 26: A019352, A019353, A019354, A019355, 30: A019356, A019357, A019358, A019359,
34: A019360, 35: A019361, 37: A019362, A019363, A019364, 40: A019365, A019366, A019367, A019368, A019369, A019370, A019371,
A019372 48: A019373, 50: A019374 A019375 A019376 A019377 A019378 A019379 A019380 A019381 A019382 A019383
A019384 A019385 A019386 A019387 A019388 A019389 A019390 A019391 A019392 A019393 A019394 A019395
A019396 A019397 A019398 A019399 A019400 A019401 A019402 80: A019403, 82: A019404 A019405 A019406 A019407
A019408 A019409 A019410 A019411 A019412 A019413 A019414 A019415 A019416 A019417 A019418 A019419
A019420 99: A019421
related: A029932 (primes with record values of the least positive prime primitive root (sic!))
A047933 A047934 A047935 A047936 A048975 A048976 A066529 A023048 A105874-A105914
primes, by primitive root: see also Artin's constant
Primes, chains of, A005603, A005602
primes, characteristic function of: A010051
Primes, compressed, A002036
primes, concatenation of: A033308
Primes, consecutive, A006549, A007700, A007513, A007529, A007530, A006489
primes, cuban: A002407*, A002648, A002504, A001479, A001480, A002367, A002368
primes, cuban, generalized: A007645*, A003627, A217035
primes, cuban, see also: A159961, A113478, A221717, A221793
primes, Cullen: A005849*, A050920*
primes, deceptive: A000864

primes, decomposition of, in quadratic fields, sequences related to:

For the field K = Q(sqrt(D)), the three columns give D, primes that decompose in K, and primes that are inert in K:
D decompose inert
-1 A002144 A002145
-2 A033200 A003628
-3 A002476 A003627
-5 A139513 A003626
-6 A157437 A191059
-7 A045386 A003625
-10 A155488 A296925
-11 A296920 A191060
-13 A296926 A296927
-14 A191017 A191061
-15 A191018 A191062
-17 A296929 A296930
-19 A191019 A191063
-22 A191020 A191064
-23 A191021 A191065
-30 A191023 A191066
-31 A191024 A191067
-35 A191026 A191068
-38 A191028 A191069
-39 A191029 A191070
-43 A191031 A184902
-46 A191032 A191071
-47 A191033 A191072
-51 A191034 A191073
-55 A191036 A191074
-59 A191038 A191075
-62 A191040 A191076
-67 A191041 A191077
-70 A191043 A191078
-71 A191044 A191079
-78 A191047 A191080
-79 A191048 A191081
-83 A191050 A191082
-86 A191051 A191083
-87 A191052 A191084
-91 A191054 A191085
-94 A191056 A191086
-95 A191057 A191087
-163 A296921 A296915
2 A001132 A003629
3 A097933 A003630
5 A045468 A003631
6 A097934 A038877
7 A296934 A003632
10 A097955 A038880
11 A296935 A296936
13 A296937 A038884
15 A097956 A038888
17 A296938 A038890
19 A297175 A297176
23 A297177 A038898
29 A191022 A038902
30 A097959 A038904
34 A191025 A038910
37 A191027 A038914
41 A191030 A038920
53 A191035 A038932
58 A191037 A038938
61 A191039 A038942
69 A191042 A038952
73 A191045 A038958
74 A191046 A038960
82 A191049 A038968
89 A191053 A038978
93 A191055 A038982
97 A191058 A038988

Primes, decompositions into, A002375, A002126, A001031, A002372, A007414
primes, differences between: A001223*, A007921*, A030173*, A037201
primes, differences between: see also primes, gaps between
primes, dihedral calculator: A038136
primes, dihedral palindromic: A048662
primes, dividing n: A001221*, A001222*, A006530*, A046660
primes, dividing Fermat numbers: A023394*, A050922, A070592, A093179, A343557
primes, dividing Fermat numbers: see also A007117, A023395, A046052, A308695, A332414, A332416, A343767, A358684
primes, doubled: A001747, A005602, A005603
primes, duodecimal: A006687
primes, Euclid-Pocklington: A053341*
primes, Euclidean: A007996
primes, even: A001747
primes, factorial: see factorial primes
primes, Fermat, generalized, see primes, generalized Fermat
primes, Fermat, generalized: A056993* A005574 A000068 A006314 A006313 A006315 A006316 A056994 A056995 A057465 A057002 A088361 A088362 A226528 A226529 A226530 A251597 A253854 A244150 A243959 A321323
primes, Fermat: A019434*, A159611
primes, Fermat: see also A093625, A138083, A171381
primes, Fibonacci numbers: A001605*, A005478*
primes, final digits of: A007652
primes, fortunate, A005235
primes, from Euclid's proof: A000945*, A000946*
primes, gaps between, sequences related to:
primes, gaps between, A001223*, A007921*, A030173*, A037201, A023200
primes, gaps between: primes beginning gaps of sizes 2, 4, ..., 64 are given in A001359, A029710, A031924, A031926, A031928 (gap 10), A031930, A031932, A031934, A031936, A031938 (gap 20), A061779, A098974, A124594, A124595, A124596 (gap 30), A126784, A134116, A134117, A134118, A126721 (gap 40), A134120, A134121, A134122, A134123, A134124 (gap 50), A204665, A204666, A204667, A204668, A126771 (gap 60), A204669, A204670.
primes, gaps between: primes beginning gaps of 70, 80,... 300: A204792, A126722, A204764, A050434 (gap 100), A204801, A204672 (gap 120), A204802, A204803, A126724 (gap 150), A184984, A204805, A204673 (gap 180), A204806, A204807 (gap 200), A224472 (gap 300).
primes, gaps between: start of the first gap of 2n: A000230, 6n: A058193, 10n: A140791, 2^n: A062529, 10^n: A101232, n^2: A138198, a^b: A123995, 128: A204812, 256: A204813.
primes, gaps between: indices of primes followed by a given gap: A029707 (gap 2), A029709 (gap 4), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).
primes, gaps between: twin primes and related: A001359, A006512, A077800, A001097, A049591, A159461
primes, gaps between, A031924 A031925 A031926 A031927 A031928 A031929 A031930 A031931 A031932 A031933 A031934 A031935 A031936 A031937 A031938 A031939
primes, gaps between, LCM of: A080374 A080375 A080376 A083273 A083552 A083551
primes, gaps between, records for: A000101* (upper end), A002386* (lower end), A005250* (gaps)
primes, gaps between, see also: A124582-A124591, A005669, A002540, A000232, A001549, A001632
primes, gaps between, see also: primes, differences between
primes, generalized Fermat: A006686, A078902, A090874, A100266, A100267, A123646
primes, generated by polynomials: see primes, produced by polynomials
primes, Germain: see primes, Sophie Germain
primes, good: A046869, A028388
primes, half-quartan: A002646
primes, happy: A035497
primes, Higgs: A007459
primes, home: A037274* (base 10), A048986* and A064795 (base 2)
primes, home, see also A048985, A064841, A195264
primes, Honaker: A033548
primes, iccanobiF: A036797
primes, in arithmetic progressions, sequences related to:
primes, in arithmetic progressions: (see also Primes in arithmetic progression)
Consider n-term arithmetic progressions (APs) of primes, i, i+d, i+2d, ..., i+(n-1)d. We can minimize (a) the first term i, (b) the common difference d, or (c) the last term, l=i+(n-1)d. This gives rise to 12 sequences since for each problem we can list the values of i, d, l, and we can list the progressions as the rows of a triangle:
problem (a) i: A007918* (assuming k-tuple conjecture), d: A061558, l: A120302, triangle: A130791
problem (b) i: A033189, d: A033188*, l: A113872, triangle: A133276
problem (c) i: A113827, d: A093364, l: A005115*, triangle: A133277
If we take the initial value to be the n-th prime (A000040) the the sequences are: d: A088430, l: A113834, triangle: A133278
One may also ask for n consecutive primes in arithmetic progression: this gives A006560 and many other sequences, see Consecutive primes in arithmetic progression for more information and references.
One may also consider n consecutive numbers in arithmetic progression having the same prime signature, and ask the same questions. This gives the following sequences:
problem (a) i: A113459, d: A113461, l: A127781, triangle: A113460
problem (b) i: A034173, d: the all-ones sequence A000012, l: A034174, triangle: A083785
problem (c) i: A087308, d: A087310, l: A133280, triangle: A086786
One may also ask for n consecutive numbers with the same prime signature: this gives sequences A034173, A034174, A083785 again. See also A087307.
See also: A031217 A033168 A033290 A033446 A033447 A033448 A033449 A033450 A033451 A035050 A035089
A035091 A035092 A035093 A035094 A035095 A035096 A047980 A047981 A047982 A052239 A052242 A052243 A053647 A054203 A057324 A057325 A057326 A057327 A057328 A057329 A057330 A057331 A057778 A057874 A058252 A058323 A058362 A059044 A266909 A293791
Primes in arithmetic progression, Consecutive primes in arithmetic progression.
Higher powers: A001912, A002496, A005574, A115104, A199307, A199364, A199365, A199366, A199367, A199368, A199369
primes, in decimal expansion of Pi: A005042
Primes, in intervals, A007491
Primes, in number fields, A003631, A003625, A003628, A003630, A003632, A003626
Primes, in residue classes, A003627, A002313, A003629, A002145, A007520, A002515, A007528, A002144, A007521, A002476, A001132, A007522, A007519
Primes, in sequences, A003032, A003033, A002072
Primes, in ternary, A001363
primes, in various ranges, sequences related to:
primes, in various ranges: (1) A003604 A006879 A006880 A007053 A007508 A033843 A035533 A036351 A036386 A039506 A039507
primes, in various ranges: (2) A040014 A049035 A049040 A050251 A050258 A050986 A050987 A052130 A055206 A055552 A055683 A055728
primes, in various ranges: (3) A055729 A055730 A055731 A055732 A055737 A055738 A057573 A057978 A058191 A058247 A058248 A060969
primes, in various ranges: (4) A060970 A060971 A063501 A064151 A066265 A066873 A071973
primes, in various ranges: (5) A091644 A091645 A091646 A091647 A091705 A091706 A091707 A091708 A091709 A091710
primes, in various ranges: (6) A091634 A091635 A091636 A091637 A091638 A091639 A091640 A091641 A091642 A091643
Primes, inert, A003631, A003625, A003628, A003630, A003632, A003626
primes, irregular: A000928*, A061576*
primes, isolated: A007510, A039818
primes, isolated: see also primes, weak
Primes, largest, A006530, A006990, A007014, A002374, A003618
primes, left-truncatable: see truncatable primes
primes, lonely: A023186, A023187, A023188
primes, long period: A006883*
primes, Lucas numbers: A001606*, A005479*
primes, Lucasian: A002515*
primes, Mersenne: A000668* (primes of form 2^p-1), A000043* (p values)
primes, Mills's: A051254*
primes, minus a constant: A000040*, A006093, A040976, A086801, A172367, A173064, A086304, A088967, A172407, A086303, A014689, A014692
primes, multiplicative and additive: A046713
primes, multiplicative: A046703
primes, next: A007918
primes, number of less than k^n: A007053, A055729, A086680, A055730, A055731, A055732, A086681, A086682, A006880, A058247, A058248, A058191
primes, number of less than n*10^k: (1) A000720*, A038801, A028505, A038812, A038813, A038814, A038815, A038816, A038817, A038818, A038819,
primes, number of less than n*10^k: (2) A038820, A038821, A038822, A080123, A080124, A080125, A080126, A080127, A080128, A080129, A116356
primes, octavan: A006686
primes, of a particular form, number that are less than or equal to 10^n: A091115 A091116 A091117 A091119-A091129 A091099 A091098 A006880 A007508
primes, of form k*n! +- 1: (1) A002981, A002982, A051915, A076133, A076679, A076134, A076680, A099350, A076681, A099351,
primes, of form k*n! +- 1: (2) A076682, A180627, A076683, A180628, A180625, A180629, A180626, A180630, A126896, A180631
primes, of form ((k+1)^n-1)/k: A028491, A004061, A004062, A004063, A004023, A005808, A004064, A016054, A006032, A006033, A006034, A006035, A127995, A127996, A127997, A127998, A127999, A128000, A098438, A128002, A128003, A128004
primes, of form n! +- 1: A002981, A002982
primes, of form x^2 + kxy + y^2: (1) A007519 A007645 A033212 A033215 A038872 A068228 A107008 A107008 A107145 A107152 A139492 A139493
primes, of form x^2 + kxy + y^2: (2) A139493 A139494 A139495 A139496 A139497 A139498 A139499 A139500 A139501 A139502 A139503 A139504
primes, of form x^2 + kxy + y^2: (3) A139505 A139506 A139507 A139508 A139509 A139510 A139511 A139512
primes, of form x^2+27y^2: A014752, A040028
primes, of form x^2+y^2: A002313*, A002331, A002330, A002144
primes, order of: A049076, A007097
primes, palindromic: A002385*, A007500, A007616
primes, palindromic: see also (1) A016041 A029971 A029972 A029973 A029974 A029975 A029976 A029977 A029978 A029979 A029980 A029981
primes, palindromic: see also (2) A029982 A029732 A046942 A046941 A050236 A050239 A039954 A118064 A119351 A016115 A050251 A050683
primes, palindromic, smoothly undulating, sequences related to:
primes, palindromic, smoothly undulating, A062209 A062210 A062211 A062212 A062213 A062214 A062215 A062216 A062217 A062218 A062219 A062220
primes, palindromic, smoothly undulating, A062221 A062222 A062223 A062224 A062225 A062226 A062227 A062228 A062229 A062230 A062231 A062232
primes, palindromic, smoothly undulating, A077799 A059758 A032758
primes, period of reciprocal of, see 1/p
primes, Pierpont: A005109
primes, primitive roots of, A001918, A002233, A002199, A002231, A001122, A007348, A003147, A001913, A001123, A007349, A001124, A001125, A001126
primes, produced by polynomials:
related to Euler's prime producing polynomial n^2 + n + 41 = A202018(n): A002837 (n^2-n+41 is prime), A005846 (primes n^2+n+41), A007634 (n^2+n+41 is composite), A056561 (n^2+n+41 is prime), A097823 (n^2+n+41 is not squarefree).
other polynomials: A007635 (primes n^2 + n + 17), A028823 (n^2 + n + 17 is prime), A048058 (n^2 + n + 11), A048059 (primes k^2 + k + 11), A048097 (n^2 + n + 11 is prime), A050268, A022464, A117081; A121887, A139414, A160548 (primes n^2 + n + 844427), A259645 (m^2+1, 3*m-1 and m^2+m+41 are prime), A005574 (k^2+1 is prime), A087370 (3m-1 is prime).
primes p such that x^2 + x + p is prime for 0 <= x <= k: A001359 (k=1), A022004 (k=2), A172454 (k=3), A187057 (k=4), A144051 (k=6), A187060 (k=7), A190800 (k=8), A191456 (k=9).
(arg) maxq min {x >= 0 | q + p*x + x^2 is composite} for given prime p: A273595 (q), A273597 (min x); for odd p: A273756 (q), A273770 (min x).
see also: primes in arithmetic progression, A033188, A033189.
Primes, products of, A007467, A006881, A006094, A007304
primes, products of: A000040 (1), A001358 (2), A014612 (3), A014613 (4)
primes, products of: For products of 1, 2, 3, 4, 5, and 6 distinct primes see A000040, A006881, A007304, A046386, A046387, and A067885, resp.
primes, pseudo: see pseudoprimes
primes, quadratic forms, discriminant:
primes, quadratic form, discriminant -104: A107132, A033218
primes, quadratic form, discriminant -108: A014752
primes, quadratic form, discriminant -112: A107133, A107134
primes, quadratic form, discriminant -116: A033219
primes, quadratic form, discriminant -11: A056874, A106857
primes, quadratic form, discriminant -120: A107135, A107136, A107137, A033220
primes, quadratic form, discriminant -124: A033221
primes, quadratic form, discriminant -128: A105389
primes, quadratic form, discriminant -12: A002476
primes, quadratic form, discriminant -132: A107138, A033222
primes, quadratic form, discriminant -136: A107139, A033223
primes, quadratic form, discriminant -140: A107140, A033224
primes, quadratic form, discriminant -144: A107141, A107142
primes, quadratic form, discriminant -148: A033225
primes, quadratic form, discriminant -152: A107143, A033226
primes, quadratic form, discriminant -156: A033227
primes, quadratic form, discriminant -15: A033212, A106858, A106859, A106860, A106861
primes, quadratic form, discriminant -160: A107144, A107145
primes, quadratic form, discriminant -164: A033228
primes, quadratic form, discriminant -168: A107146, A107147, A107148, A033229
primes, quadratic form, discriminant -16: A002144, A002313
primes, quadratic form, discriminant -172: A033230
primes, quadratic form, discriminant -176: A107149, A107150
primes, quadratic form, discriminant -180: A107151, A107152
primes, quadratic form, discriminant -184: A107153, A033231
primes, quadratic form, discriminant -188: A033232
primes, quadratic form, discriminant -192: A107154
primes, quadratic form, discriminant -196: A107155
primes, quadratic form, discriminant -19: A106862, A106863
primes, quadratic form, discriminant -200: A107156, A107157
primes, quadratic form, discriminant -204: A107158, A033233
primes, quadratic form, discriminant -208: A107159, A107160
primes, quadratic form, discriminant -20: A033205, A106864, A106865
primes, quadratic form, discriminant -212: A033234
primes, quadratic form, discriminant -216: A107161, A107162
primes, quadratic form, discriminant -220: A033235
primes, quadratic form, discriminant -224: A107163, A107164
primes, quadratic form, discriminant -228: A107165, A033236
primes, quadratic form, discriminant -232: A107166, A033237
primes, quadratic form, discriminant -236: A033238
primes, quadratic form, discriminant -23: A106866, A106867, A106868, A106869
primes, quadratic form, discriminant -240: A107167, A107168, A107169
primes, quadratic form, discriminant -244: A033239
primes, quadratic form, discriminant -248: A107170, A033240
primes, quadratic form, discriminant -24: A033199, A084865
primes, quadratic form, discriminant -256: A014754
primes, quadratic form, discriminant -260: A107171, A033241
primes, quadratic form, discriminant -264: A107172, A107173, A107174, A033242
primes, quadratic form, discriminant -268: A033243
primes, quadratic form, discriminant -272: A107175, A107176
primes, quadratic form, discriminant -276: A107177, A033244
primes, quadratic form, discriminant -27: A002476, A106870
primes, quadratic form, discriminant -280: A107178, A107179, A107180, A033245
primes, quadratic form, discriminant -284: A033246
primes, quadratic form, discriminant -288: A107181
primes, quadratic form, discriminant -28: A033207
primes, quadratic form, discriminant -292: A033247
primes, quadratic form, discriminant -296: A107182, A033248
primes, quadratic form, discriminant -300: A107183, A107184
primes, quadratic form, discriminant -304: A107185, A107186
primes, quadratic form, discriminant -308: A107187, A033249
primes, quadratic form, discriminant -312: A107188, A107189, A107190, A033250
primes, quadratic form, discriminant -316: A033251
primes, quadratic form, discriminant -31: A033221, A106871, A106872, A106873, A106874
primes, quadratic form, discriminant -320: A107191, A107192
primes, quadratic form, discriminant -324: A107193
primes, quadratic form, discriminant -328: A107194, A033252
primes, quadratic form, discriminant -32: A007519, A007520, A106875, A106876
primes, quadratic form, discriminant -332: A033253
primes, quadratic form, discriminant -336: A107195, A107196, A107197, A107198
primes, quadratic form, discriminant -340: A107199, A033254
primes, quadratic form, discriminant -344: A107200, A033255
primes, quadratic form, discriminant -348: A033256
primes, quadratic form, discriminant -352: A107201, A107202
primes, quadratic form, discriminant -356: A033257
primes, quadratic form, discriminant -35: A106877, A106878, A106879, A106880, A106881
primes, quadratic form, discriminant -360: A107203, A107204, A107205, A107206
primes, quadratic form, discriminant -364: A107207, A033258
primes, quadratic form, discriminant -368: A107208, A107209
primes, quadratic form, discriminant -36: A040117, A068228, A106882
primes, quadratic form, discriminant -372: A107210, A033202
primes, quadratic form, discriminant -376: A107211, A033204
primes, quadratic form, discriminant -380: A033206
primes, quadratic form, discriminant -384: A107212, A107213
primes, quadratic form, discriminant -388: A033208
primes, quadratic form, discriminant -392: A107214, A107215
primes, quadratic form, discriminant -396: A107216, A107217
primes, quadratic form, discriminant -39: A033227, A106883, A106884, A106885, A106886, A106887, A106888
primes, quadratic form, discriminant -3: A007645
primes, quadratic form, discriminant -400: A107218, A107219
primes, quadratic form, discriminant -40: A033201, A106889
primes, quadratic form, discriminant -43: A106890, A106891
primes, quadratic form, discriminant -44: A033209, A106282, A106892, A106893
primes, quadratic form, discriminant -47: A033232, A106894, A106895, A106896, A106897, A106898, A106899, A106900
primes, quadratic form, discriminant -48: A068229
primes, quadratic form, discriminant -4: A002313
primes, quadratic form, discriminant -51: A106901, A106902, A106903, A106904
primes, quadratic form, discriminant -52: A033210, A106905, A106906
primes, quadratic form, discriminant -55: A033235, A106907, A106908, A106909, A106910, A106911, A106912, A106913
primes, quadratic form, discriminant -56: A033211, A106914, A106915, A106916, A106917
primes, quadratic form, discriminant -59: A106918, A106919, A106920, A106921, A106922
primes, quadratic form, discriminant -63: A106923, A106924, A106925, A106926, A106927, A106928, A106929, A106930
primes, quadratic form, discriminant -64: A007521, A106931
primes, quadratic form, discriminant -67: A106932, A106933
primes, quadratic form, discriminant -68: A033213, A106934, A106935, A106936, A106937, A106938
primes, quadratic form, discriminant -71: A033246, A106939, A106940, A106941, A106942, A106943, A106944, A106945, A106946, A106947, A106948
primes, quadratic form, discriminant -72: A106949, A106950
primes, quadratic form, discriminant -75: A033212, A106951, A106952
primes, quadratic form, discriminant -76: A033214, A106953, A106954, A106955
primes, quadratic form, discriminant -79: A033251, A106956, A106957, A106958, A106959, A106960, A106961, A106962
primes, quadratic form, discriminant -7: A045373, A106856
primes, quadratic form, discriminant -80: A047650, A106963, A106964, A106965
primes, quadratic form, discriminant -83: A106966, A106967, A106968, A106969, A106970
primes, quadratic form, discriminant -84: A033215, A102271, A102273, A106971, A106972, A106973, A106974
primes, quadratic form, discriminant -87: A033256, A106975, A106976, A106977, A106978, A106979, A106980, A106981, A106982, A106983
primes, quadratic form, discriminant -88: A033216, A106984
primes, quadratic form, discriminant -8: A033203
primes, quadratic form, discriminant -91: A106985, A106986, A106987, A106988, A106989
primes, quadratic form, discriminant -92: A033217
primes, quadratic form, discriminant -95: A033206, A106990, A106991, A106992, A106993, A106994, A106995, A106996, A106997, A106998, A106999, A107000, A107001
primes, quadratic form, discriminant -96: A107002, A107003, A107004, A107005, A107006, A107007, A107008
primes, quadratic form, discriminant -99: A107009, A107010, A107011, A107012, A107013
primes, quadratic form, discriminant 1020: A139512
primes, quadratic form, discriminant 117: A139494
primes, quadratic form, discriminant 140: A139495
primes, quadratic form, discriminant 165: A139496
primes, quadratic form, discriminant 21: A139492
primes, quadratic form, discriminant 221: A139497
primes, quadratic form, discriminant 285: A139498
primes, quadratic form, discriminant 357: A139499
primes, quadratic form, discriminant 396: A139500
primes, quadratic form, discriminant 437: A139501
primes, quadratic form, discriminant 480: A139502
primes, quadratic form, discriminant 525: A139503
primes, quadratic form, discriminant 572: A139504
primes, quadratic form, discriminant 621: A139505
primes, quadratic form, discriminant 672: A139506
primes, quadratic form, discriminant 725: A139507
primes, quadratic form, discriminant 77: A139493
primes, quadratic form, discriminant 780: A139508
primes, quadratic form, discriminant 837: A139509
primes, quadratic form, discriminant 896: A139510
primes, quadratic form, discriminant 957: A139511
Primes, quadratic partitions of, A002973, A002972
Primes, quadratic residues of, A002223, A002224, A002225, A002226, A002228, A002227
primes, quartan: A002645
primes, quintan: A002649, A002650
primes, reciprocals of, periods: see 1/p
primes, regular: A007703*
Primes, represented by quadratic forms, A002496, A007645, A002383, A007490, A002327, A005473, A005471, A007635, A007639, A007637, A007641, A005846
primes, repunit: A004022*, A004023*
primes, right-truncatable: see truncatable primes
primes, safe: A005385*, A051900, A051901, A051902
primes, sextan: A002647
primes, short period: A006559*
Primes, single, A007510
primes, Sophie Germain: A005384
Primes, special sequences of, A001259, A001275
Primes, square roots of, A000006
primes, Stern: A042978
primes, strobogrammatic: A007597, A018847
primes, strong: A051634
primes, sum of the first k^n primes, k=2,3,5,6,7,10: A099825, A099826, A113633, A113634, A113635, A099824
Primes, sums of digits of, A007605
Primes, sums of, A007610, A001414, A007504, A007468, A002373, A001043, A001172
Primes, sums of, divisibility: see Index to sums of powers of primes divisibility sequences
primes, sums of, minimizing: A022894, A083309, A113040, A215036, A215029, A215030
Primes, supersingular, A006962
primes, that divide sum of all primes <= p: A007506, A024011, A028581, A028582
Primes, to odd powers only, A002035
primes, transformed by cellular automata: A093510 A093511 A093512 A093513 A093514 A093515 A093516 A093517
primes, transforms of, A007442, A007444, A007447, A007441, A007445, A007296, A007446
primes, truncatable: see truncatable primes
primes, truncated: see truncatable primes
primes, twin primes conjecture: see also A093483
primes, twin: A001359*, A014574*, A006512*, A001097*, A077800
primes, twin: see also twin primes constant
primes, twin: see also A005597, A007508, A033843, A036061, A036062, A036063
primes, undulating: A039944
primes, various subsets in range 2^n,2^(n+1), sequences related to:
primes, various subsets in range 2^n,2^(n+1): (A-numbers in parentheses give the primes whose occurrences are being counted)
A036378* (A000040), A095005 (A027697), A095006 (A027699), A095007 (A002144), A095008 (A002145), A095009 (A007519), A095010 (A007520), A095011 (A007521), A095012 (A007522), A095013 (A001132), A095014 (A003629), A095015 (A002476), A095016 (A007528), A095017 (A001359), A095018 (A066196), A095019 (A095071), A095020 (A095070), A095021 (A030430), A095022 (A030432), A095023 (A030431), A095024 (A030433), A095052 (A095072), A095053 (A095073), A095054 (A095074), A095055 (A095075), A095056 (A081091), A095057 (A095077), A095058 (A095078), A095059 (A095079), A095060 (A095080), A095061 (A095081), A095062 (A095082), A095063 (A095083), A095064 (A095084), A095065 (A095085), A095066 (A095086), A095067 (A095087), A095068 (A095088), A095069 (A095089), A095092 (A095102), A095093 (A095103), A095094 (A080114), A095095 (A080115)
primes, weak or weakly: A050249, A051635, A137985, A158124, A158125, A186995, A192545; see also A158641, A253269, A323745
primes, weakly prime numbers: A050249
primes, which are average of their neighbors: A006562
primes, whose reversal is a square, A007488
primes, Wilson: A007540*
Primes, with consecutive digits, A006510, A006055
primes, with embedded primes:
(permutation): A039993, A080603, A080608.
(substring): A033274, A034844, A039992, A039994, A039996, A039998, A045719, A079397, A092621, A092622, A092623, A092628, A109066, A134596, A137812,
A152313, A152426, A152427, A155024, A168169, A178596, A178597, A179336, A179909, A179910, A179911, A179912, A179913, A179914, A179915, A179916, A179917, A179918, A179919, A179920, A179922, A179924*
primes, with first digit 1 (or 2, 3, etc.): A045707, A045708, A045709, etc.
Primes, with large least nonresidues, A002225, A002226, A002228, A002227
Primes, with prime subscripts, A006450
primes, Woodall: A002234*, A050918*
primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, sequences related to:
primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,...:
A000043 A001770 A001771 A001772 A001773 A001774 A001775 A002235 A002236 A002237 A002238 A002240 A002242 A002253 A002254 A002256 A002258 A002259 A002261 A002269 A002274
A032353 A032356 A032359 A032360 A032361 A032362 A032363 A032364 A032365 A032366 A032367 A032368 A032370 A032371 A032372 A032373 A032374 A032375 A032376 A032377 A032379 A032380 A032381 A032382 A032383 A032384 A032385 A032386 A032387 A032388 A032389 A032390 A032391 A032392 A032393 A032394 A032395 A032396 A032397 A032398 A032399 A032400 A032401 A032402 A032403 A032404 A032405 A032406 A032407 A032408 A032409 A032410 A032411 A032412 A032413 A032414 A032415 A032416 A032417 A032418 A032419 A032420 A032421 A032422 A032423 A032424 A032425
A032453 A032454 A032455 A032456 A032457 A032458 A032459 A032460 A032461 A032462 A032464 A032465 A032466 A032467 A032468 A032469 A032470 A032471 A032472 A032473 A032474 A032475 A032476 A032477 A032478 A032479 A032480 A032481 A032482 A032483 A032484 A032485 A032486 A032487 A032488 A032489 A032490 A032491 A032492 A032493 A032494 A032495 A032496 A032497 A032498 A032499 A032500 A032501 A032502 A032503 A032504 A032507
A046758 A050537 A050538 A050539 A050540 A050541 A050543 A050544 A050545 A050546 A050547
A050549 A050550 A050551 A050552 A050553 A050554 A050555 A050556 A050557 A050558 A050559 A050560 A050561 A050562 A050563 A050564 A050565 A050566 A050567 A050568 A050569 A050570 A050571 A050572 A050573 A050574 A050575 A050576 A050577 A050578 A050579 A050580 A050581 A050582 A050583 A050584 A050585 A050586 A050587 A050588 A050589 A050590 A050591 A050592 A050593 A050594 A050595 A050596 A050597 A050598 A050599
A050616 A050617 A050618 A050619
A050830 A050831 A050832 A050833 A050834 A050835 A050836 A050837 A050838 A050839 A050840 A050841 A050842 A050843 A050844 A050845 A050846 A050847 A050848 A050849 A050850 A050851 A050852 A050853 A050854 A050855 A050856 A050857 A050858 A050859 A050860 A050861 A050862 A050863 A050864 A050865 A050866 A050867 A050868 A050869
A050877 A050878 A050879 A050880 A050881 A050882 A050883 A050884 A050885 A050886 A050887 A050888 A050889 A050890 A050891 A050892 A050893 A050894 A050895 A050896 A050897 A050898 A050899 A050900 A050901 A050902 A050903 A050904 A050905 A050906 A050907 A050908
A053345 A053346 A053348 A053349 A053350 A053351 A053352 A053353 A053354 A053355 A053356 A053357 A053358 A053359 A053360 A053361 A053362 A053363 A053364 A053365 A053366
A007505 A050522 A050523 A050524 A050525 A050526 A050527 A050528 A002255 A050413
Primes: A005361, A002200, A002038, A007445, A007296, A001259, A006450, A001275

primeth recurrence: A007097*
primitive (1): A000020, A003050, A002233, A002199, A000019, A005992, A001578, A006246, A006245, A002589
primitive (2): A001122, A007348, A006248, A006991, A006039, A006036, A001913, A001123, A007627, A006576, A007349, A001124, A001125, A002975, A001126
Primitive factors, A002185, A007138, A002184
primitive polynomials: see also trinomials over GF(2)

primitive roots, sequences related to:

primitive roots, primes by: see primes by primitive root
primitive roots: A060749*, A001918*, A002199, A002229, A002230, A002231, A029932, A071894

primorial base, sequences related to:

primorial base: A049345*
primorial base, digit sum: A276150
primorial base, digits as table: A235168
primorial base, number of nonzero digits: A267263
primorial base, number of significant digits: A235224
primorial base, number of trailing zeros: A276084*, A257993
primorial base, prime-factorization encodings of related polynomials: A276086
primorial base, shift left operation (append 0 to right): A276154
primorial base, the least significant digit: A000035
primorial base, the least significant nonzero digit: A276088
primorial base, the least significant nonzero digit decremented by one: A276151
primorial base, the least significant nonzero digit replaced by zero: A276093
primorial base, the most significant digit: A276153
primorial base, with pattern, digits in maximal descending sequence ..6421: A057588
primorial base, with pattern, no digits larger than one: A276156
primorial base, with pattern, one 1 and the rest zeros: A002110
primorial base, with pattern, only one nonzero digit: A060735
primorial base, with pattern, repunits: A143293

primorial numbers, sequences related to:

primorial numbers: A002110*, A034386*
primorial numbers: see also A056113, A056129, A006862, A057588, A129912
primorial primes: A005234*, A014545*, A018239*, A006794*, A057704*, A057705*, A057706

principal character: A005368
prism numbers: A005914, A005915, A005919, A005920

[ Aa | Ab | Al | Am | Ap | Ar | Ba | Be | Bi | Bl | Bo | Br | Ca | Ce | Ch | Cl | Coa | Coi | Com | Con | Cor | Cu | Cy | Da | De | Di | Do | Ea | Ed | El | Eu | Fa | Fe | Fi | Fo | Fu | Ga | Ge | Go | Gra | Gre | Ha | He | Ho | Ia | In | J | K | La | Lc | Li | Lo | Lu | M | Mag | Map | Mat | Me | Mo | Mu | N | Na | Ne | Ni | No | Nu | O | Pac | Par | Pas | Pea | Per | Ph | Poi | Pol | Pos | Pow | Pra | Pri | Pro | Ps | Qua | Que | Ra | Rea | Rel | Res | Ro | Ru | Sa | Se | Si | Sk | So | Sp | Sq | St | Su | Sw | Ta | Te | Th | To | Tra | Tri | Tu | U | V | Wa | We | Wi | X | Y | Z | 1 | 2 | 3 | 4 ]