Factorizations of prime(n)! / prime(n)# + 1 for n = 1 to 26
       ===========================================================


Contents:                                    page

       Table                                    2
       n = 1,2,3    p = 2,3,5                   3
       n = 4,5,6    p = 7,11,13                 4
       n = 7,8      p = 17,19                   5
       n = 9,10     p = 23,29                   6
       n = 11       p = 31                      7
       n = 12       p = 37                      8
       n = 13       p = 41                      9
       n = 14       p = 43                     10
       n = 15       p = 47                     11
       n = 16       p = 53                     12
       n = 17       p = 59                     13
       n = 18       p = 61                     14
       n = 19       p = 67                     15
       n = 20       p = 71                     16
       n = 21       p = 73                     17
       n = 22       p = 79                     18
       n = 23       p = 83                     19
       n = 24       p = 89                     20
       n = 25       p = 97                     21
       n = 26       p = 101                    22
       n = 27       p = 103                    23





All factorizations by using Dario Alpern's ECM-program
http://www.alpertron.com.ar/ECM.HTM



A103890.txt
Reinhard Zumkeller (reinhard.zumkeller@lhsystems.com), Feb 20 2005



                                                                 page 2



+----+------------+------------+------------+------------+------------+
|    | A103890(n) | A103891(n) | A103892(n) | A103893(n) | A103894(n) | 
| n  +------------+------------+------------+------------+------------+
|    |            |            prime factors             | number of  | 
|    | p=prime(n) | smallest   | greatest   | # distinct | divisors   | 
|    |            |------------+------------+------------+------------+
|    | x=p!/p#+1  | A020639(x) | A006530(x) | A001221(x) | A000005(x) | 
+----+------------+------------+------------+------------+------------+
|  1 |          2 |          2 |          2 |          1 |          2 |
|  2 |          2 |          2 |          2 |          1 |          2 |
|  3 |          5 |          5 |          5 |          1 |          2 |
|  4 |         25 |          5 |          5 |          1 |          3 |
|  5 |      17281 |         11 |       1571 |          2 |          4 |
|  6 |     207361 |          7 |       2693 |          3 |          8 |
|  7 |  696729601 |         19 |      15427 |          3 |          8 |
|  8 |12541132801 |         31 |      27749 |          4 |         16 |
|  9 |   [Len=15] |      27893 | 4154449757 |          2 |          4 |
| 10 |   [Len=22] |        223 |   [Len=15] |          3 |          8 |
| 11 |   [Len=23] |     554797 |   [Len=17] |          2 |          4 |
| 12 |   [Len=31] |      10333 |   [Len=14] |          4 |         16 |
| 13 |   [Len=36] |         29 |   [Len=19] |          4 |         16 |
| 14 |   [Len=37] |         61 |   [Len=19] |          5 |         32 |
| 15 |   [Len=42] |   28652131 |   [Len=23] |          3 |          8 |
| 16 |   [Len=51] |  293049347 |   [Len=42] |          2 |          4 |
| 17 |   [Len=59] |    7731517 |   [Len=41] |          3 |          8 |
| 18 |   [Len=61] |       1483 |   [Len=41] |          4 |         16 |
| 19 |   [Len=70] |         73 |   [Len=39] |          6 |         64 |
| 20 |   [Len=76] |   [Len=12] |   [Len=22] |          5 |         32 |
| 21 |   [Len=78] |         67 |   [Len=63] |          5 |         32 |
| 22 |   [Len=87] |     440939 |   [Len=33] |          5 |         32 |
| 23 |   [Len=93] |       1321 |   [Len=60] |          5 |         32 |
| 24 |  [Len=102] |      94099 |   [Len=36] |          6 |         64 |
| 25 |  [Len=116] |         89 |   [Len=99] |          5 |         32 |
| 26 |  [Len=122] |        107 |  [Len=104] |          4 |         16 |
| 27 |  [Len=124] |        281 |  [Len=102] |          5 |         32 |
+----+------------+------------+------------+------------+------------+


Len = number of digits in decimal representation (A055642),
e.g. A103890(9) = 23!/23#+1 = 115880067072001 with Len=15.



-----------                       -------------------            page 3
2! / 2# + 1                       n = 1: prime(1) = 2
-----------                       -------------------

2! = 2;  2# = 2

2! / 2# + 1 = 2 

omega = 1;  Omega = 1;  mu = -1;  tau = 2

sigma = 3;  phi = 1

=======================================================================


-----------                       ------------------- 
3! / 3# + 1                       n = 2: prime(2) = 3 
-----------                       ------------------- 

3! = 6;  3# = 6

3! / 3# + 1 = 2 

omega = 1;  Omega = 1;  mu = -1;  tau = 2

sigma = 3;  phi = 1

=======================================================================


-----------                       ------------------- 
5! / 5# + 1                       n = 3: prime(3) = 5 
-----------                       ------------------- 

5! = 120;  5# = 30

5! / 5# + 1 = 5 

omega = 1;  Omega = 1;  mu = -1;  tau = 2

sigma = 6;  phi = 4

=======================================================================


-----------                       -------------------            page 4
7! / 7# + 1                       n = 4: prime(4) = 7 
-----------                       ------------------- 

7! = 5040;  7# = 210

7! / 7# + 1 = 25 

Factorization
#1: 5^2

omega = 1;  Omega = 2;  mu = 0;  tau = 3

sigma = 31;  phi = 20

=======================================================================


-------------                     -------------------- 
11! / 11# + 1                     n = 5: prime(5) = 11 
-------------                     -------------------- 

11! = 39 916800;  11# = 2310

11! / 11# + 1 = 17281

Factorization
#1: 11
#2: 1571

omega = 2;  Omega = 2;  mu = +1;  tau = 4

sigma = 18864;  phi = 15700

=======================================================================


-------------                     -------------------- 
13! / 13# + 1                     n = 6: prime(6) = 13 
-------------                     -------------------- 

13! = 6227 020800;  13# = 30030

13! / 13# + 1 = 207361

Factorization
#1: 7
#2: 11
#3: 2693

omega = 3;  Omega = 3;  mu = -1;  tau = 8;  

sigma = 258624;  phi = 161520

=======================================================================


-------------                     --------------------           page 5
17! / 17# + 1                     n = 7: prime(7) = 17 
-------------                     -------------------- 

17! = 355 687428 096000;  17# = 510510
               [Len=15]

17! / 17# + 1 = 696 729601

Factorization
#1: 19
#2: 2377
#2: 15427

omega = 3;  Omega = 3;  mu = -1;  tau = 8

sigma = 733755680;  phi = 659739168

=======================================================================


-------------                     -------------------- 
19! / 19# + 1                     n = 8: prime(8) = 19 
-------------                     -------------------- 

19! = 121645 100408 832000;  19# = 9 699690
                  [Len=18]

19! / 19# + 1 = 12541 132801
                    [Len=11]

Factorization
#1: 31
#2: 61 
#3: 239
#4: 27749

omega = 4;  Omega = 4;  mu = +1;  tau = 16

sigma = 13213 440000;  phi = 11887 243200
            [Len=11]             [Len=11]

=======================================================================


-------------                     --------------------           page 6
23! / 23# + 1                     n = 9: prime(9) = 23
-------------                     -------------------- 

23! = 25852 016738 884976 640000;  23# = 223 092870
                        [Len=23]

23! / 23# + 1 = 115 880067 072001
                         [Len=15]

Factorization
#1: 27893 
#2: 4154 449757
       [Len=10]

omega = 2;  Omega = 2;  mu = +1;  tau = 4

sigma = 115 884221 549652;  phi = 115 875912 594352
                 [Len=15]                  [Len=15]

=======================================================================


-------------                    ---------------------- 
29! / 29# + 1                    n = 10: prime(10) = 29 
-------------                    ---------------------- 

29! = 8 841761 993739 701954 543616 000000
                                  [Len=31]

29# = 6469 693230
         [Len=10]

29! / 29# + 1 = 1366 643159 020339 200001
                                 [Len=22]

Factorization
#1: 223
#2: 40429 
#3: 151 585363 459003
             [Len=15]

omega = 3;  Omega = 3;  mu = -1;  tau = 8

sigma = 1372 805558 801047 105280
                         [Len=22]

phi = 1360 481062 410358 294032
                       [Len=22]

=======================================================================


-------------                    ----------------------          page 7
31! / 31# + 1                    n = 11: prime(11) = 31 
-------------                    ---------------------- 

31! = 8222 838654 177922 817725 562880 000000
                                     [Len=34]

31# = 200560 490130
           [Len=12]

31! / 31# + 1 = 40999 294770 610176 000001
                                  [Len=23]

Factorization
#1: 554797 
#2: 73899 633146 196133
               [Len=17]

omega = 2;  Omega = 2;  mu = +1;  tau = 4

sigma = 40999 368670 243322 750932
                          [Len=23]

phi = 40999 220870 977029 249072
                        [Len=23]

=======================================================================


-------------                    ----------------------          page 8
37! / 37# + 1                    n = 12: prime(12) = 37 
-------------                    ---------------------- 

37! = 13 763753 091226 345046 315979 581580 902400 000000
                                                 [Len=44]

37# = 7 420738 134810
             [Len=13]

37! / 37# + 1 = 1 854768 736099 424576 471040 000001
                                            [Len=31]

Factorization
#1: 10333
#2: 17551 
#3: 412 876421
#4: 24 770877 398207
            [Len=14]

omega = 4;  Omega = 4;  mu = +1;  tau = 16

sigma = 1 855053 929165 456908 669711 085568
                                    [Len=31]

phi = 1 854483 563489 396099 991763 032000
                                  [Len=31]

=======================================================================


-------------                    ----------------------          page 9
41! / 41# + 1                    n = 13: prime(13) = 41 
-------------                    ---------------------- 

41! = 33 452526 613163 807108 170062 053440 751665 152000 000000
                                                        [Len=50]

41# = 304 250263 527210
               [Len=15]


41! / 41# + 1 = 109950 690675 973888 893203 251200 000001
                                                 [Len=36]

Factorization
#1: 29
#2: 743 
#3: 3 570470 221379
#4: 1 429176 066859 677377
                  [Len=19]

omega = 4;  Omega = 4;  mu = +1;  tau = 16

sigma = 113895 178720 398409 713058 206857 404800
                                         [Len=36]

phi = 106016 408292 727234 808287 504322 403328
                                       [Len=36]

=======================================================================


-------------                    ----------------------         page 10
43! / 43# + 1                    n = 14: prime(14) = 43 
-------------                    ---------------------- 



43! = 60415 263063 373835 637355 132068 513997 507264 512000 000000
                                                           [Len=53]

43# = 13082 761331 670030
                 [Len=17]

43! / 43# + 1 =  4 617929 008390 903333 514536 550400 000001
                                                    [Len=37]

Factorization
#1: 61
#2: 613 
#3: 1 100653
#4: 14 481017
#5: 7 748318 379505 746557
                  [Len=19]

omega = 5;  Omega = 5;  mu = -1;  tau = 32

sigma = 4 701294 182073 054820 056713 442085 236768
                                           [Len=37]

phi = 4 534810 991759 912394 035394 805790 730240
                                         [Len=37]

=======================================================================


-------------                    ----------------------         page 11
47! / 47# + 1                    n = 15: prime(15) = 47 
-------------                    ---------------------- 

47! = 258623 241511 168180 642964 355153 611979 969197 632389 
      120000 000000
                                                     [Len=60]

47# = 614889 782588 491410
                  [Len=18]

47! / 47# + 1 = 420600 974084 243475 616503 989010 432000 000001 
                                                        [Len=42]

Factorization
#1: 28 652131
#2: 677643 511121
#3: 21662 673895 172922 098651
                      [Len=23]

omega = 3;  Omega = 3;  mu = -1;  tau = 8

sigma = 420600 988764 434556 002649 278043 833454 083808
                                                [Len=42]

phi = 420600 959404 052395 273684 047768 731734 440000
                                              [Len=42]

=======================================================================


-------------                    ----------------------         page 12
53! / 53# + 1                    n = 16: prime(16) = 53 
-------------                    ---------------------- 

53! =   4274 883284 060025 564298 013753 389399 649690 343788 366813 
      724672 000000 000000
                                                            [Len=70]

53# = 32 589158 477190 044730
                     [Len=20]

53! / 53# + 1 =    131 175012 912718 250806 592304 873426 282086 
                400000 000001
                                                        [Len=51]

Factorization
#1: 293 049347
#2: 447620 901583 917369 406703 727865 417431 168683
                                            [Len=42]

omega = 2;  Omega = 2;  mu = +1;  tau = 4

sigma = 131 175013 360339 152390 509674 280130 009951 817724 218032
                                                           [Len=51]

phi = 131 175012 465097 349222 674935 466722 554220 982275 781972
                                                         [Len=51]

=======================================================================


-------------                    ----------------------         page 13
59! / 59# + 1                    n = 17: prime(17) = 59 
-------------                    ---------------------- 

59! =    138 683118 545689 835737 939019 720389 406345 902876 772687 
      432540 821294 940160 000000 000000
                                                            [Len=81]

59# = 1922 760350 154212 639070
                       [Len=22]

59! / 59# + 1 =  72127 095056 108748 061547 940676 488545 036232 
                818688 000000 000001
                                                        [Len=59]

Factorization
#1: 7 731517
#2: 347785 835587
#3: 26823 894708 473887 265117 477378 744683 922119
                                           [Len=41]

omega = 3;  Omega = 3;  mu = -1;  tau = 8

sigma =  72127 104385 286772 370615 263357 328839 468994 235929 
        957013 958080
                                                       [Len=59]

phi =  72127 085726 930723 806128 407412 596025 133706 356204 
      227941 020368
                                                     [Len=59]

=======================================================================


-------------                    ----------------------         page 14
61! / 61# + 1                    n = 18: prime(18) = 61 
-------------                    ---------------------- 

61! = 507580 213877 224798 800856 812176 625227 226004 528988 036003 
      099405 939480 985600 000000 000000
                                                            [Len=84]

61# = 117288 381359 406970 983270
                         [Len=24]

61! / 61# + 1 =      4 327625 703366 524883 692876 440589 312702 
                173969 121280 000000 000001 
                                                        [Len=61]

Factorization
#1: 1483 
#2: 7127 
#3: 7 008809 876989
#4: 58419 455175 821973 834615 220346 798867 768249
                                           [Len=41]

omega = 4;  Omega = 4;  mu = +1;  tau = 16

sigma =      4 331151 484674 765440 661947 496309 232509 572841 941130 
        209291 760000
                                                              [Len=61]

phi =      4 324100 740959 994221 941239 110029 140624 838195 439409 
      501080 221568
                                                            [Len=61]

=======================================================================


-------------                    ----------------------         page 15
67! / 67# + 1                    n = 19: prime(19) = 67 
-------------                    ---------------------- 

67! =  36471 110918 188685 288249 859096 605464 427167 635314 049524 
      593701 628500 267962 436943 872000 000000 000000
                                                            [Len=95]

67# = 7 858321 551080 267055 879090
                           [Len=25]

67! / 67# + 1 =   4641 081518 632318 859492 593303 493155 822657 
                704661 332315 340800 000000 000001 
                                                        [Len=70]

Factorization
#1: 73 
#2: 463 
#3: 292069 
#4: 1 485559
#5: 1684 513433 610479
#6: 187 873487 957710 251112 719111 051932 885411
                                         [Len=39]

omega = 6;  Omega = 6;  mu = +1;  tau = 64

sigma =   4714 838542 729049 076050 633579 797208 711316 188355 531786 
        143035 007987 712000
                                                              [Len=70]

phi =   4567 599725 971282 082891 714564 566159 491163 232096 471032 
      203915 836492 551680
                                                            [Len=70]

=======================================================================


-------------                    ----------------------         page 16
71! / 71# + 1                    n = 20: prime(20) = 71 
-------------                    ---------------------- 

71! = 850478 588567 862317 521167 644239 926010 288584 608120 796235 
      886430 763388 588680 378079 017697 280000 000000 000000
                                                           [Len=102]

71# = 557 940830 126698 960967 415390
                             [Len=27]

71! / 71# + 1 =   1524 316813 979598 806211 747344 599292 098393 
                696518 967985 650532 352000 000000 000001
                                                        [Len=76]

Factorization
#1: 337809 273983
#2: 5 530881 877187
#3: 31 734470 040281
#4: 10638 349187 975557
#5: 2416 594580 545944 177593
                     [Len=22]

omega = 5;  Omega = 5;  mu = -1;  tau = 32

sigma =   1524 316813 984434 943298 474956 333546 576264 648335 538343 
        359387 327016 533991 436288
                                                              [Len=76]

phi =   1524 316813 974762 669125 021667 221733 459675 731931 826330 
      862642 208638 346306 309120
                                                            [Len=76]

=======================================================================


-------------                    ----------------------         page 17
73! / 73# + 1                    n = 21: prime(21) = 73 
-------------                    ---------------------- 

73! =   4470 115461 512684 340891 257138 125051 110076 800700 282905 
      015819 080092 370422 104067 183317 016903 680000 000000 000000
                                                           [Len=106]

73# = 40729 680599 249024 150621 323470
                               [Len=29]

73! / 73# + 1 = 109750 810606 531114 047245 808811 149031 084346 
                149365 694966 838329 344000 000000 000001 
                                                        [Len=78]

Factorization
#1: 67 
#2: 1861 
#3: 8539 
#4: 678253 
#5:    151 980484 198948 823551 696833 505973 
    745524 167842 228692 010030 901969
                                     [Len=63]

omega = 5;  Omega = 5;  mu = -1;  tau = 32

sigma = 111461 952791 070229 304005 829509 981995 239183 374051 698309 
        575695 450501 005140 643200
                                                              [Len=78]

phi = 108041 831366 305927 381253 035388 442403 103883 841243 974396 
      796749 181454 414328 007680
                                                            [Len=78]

=======================================================================


-------------                    ----------------------         page 18
79! / 79# + 1                    n = 22: prime(22) = 79 
-------------                    ---------------------- 

79! =    894 618213 078297 528685 144171 539831 652069 808216 779571 
      907213 868063 227837 990693 501860 533361 810841 010176 000000 
      000000 000000
                                                           [Len=117]

79# = 3 217644 767340 672907 899084 554130
                                  [Len=31]

79! / 79# + 1 =    278 035108 834491 952374 200462 632195 223836 
                131498 049515 522896 518347 698995 200000 000000 
                000001
                                                        [Len=87]

Factorization
#1: 440939 
#2: 229 918267
#3: 1 800121 214093
#4: 3745 828933 595186 733991 167749
#5: 406 722276 544872 969063 670718 259161
                                  [Len=33]

omega = 5;  Omega = 5;  mu = -1;  tau = 32

sigma =    278 035740 596245 831054 283943 139751 395511 341437 099068 
        804021 560315 995511 808224 120644 240000
                                                              [Len=87]

phi =    278 034477 072743 559408 826422 312502 996081 319735 887546 
      173796 087019 613617 593641 525557 076480 
                                                            [Len=87]

=======================================================================


-------------                    ----------------------         page 19
83! / 83# + 1                    n = 23: prime(23) = 83 
-------------                    ---------------------- 

83! =  39455 239697 206586 511897 471180 120610 571436 503407 643446 
      275224 357528 369751 562996 629334 879591 940103 770870 906880 
      000000 000000 000000
                                                           [Len=125]

83# = 267 064515 689275 851355 624017 992790
                                    [Len=33]

83! / 83# + 1 =    147 736735 430295 643813 555157 824243 254137 
                566832 803590 568246 293989 233338 089472 000000 
                000000 000001 
                                                        [Len=93]

Factorization
#1: 1321 
#2: 3011 
#3: 19433 
#4: 11078 093307 398182 946017
#5: 172532 158443 057699 772164 532525 607875 550686 109683 
    184687 080411
                                                   [Len=60]

omega = 5;  Omega = 5;  mu = -1;  tau = 32

sigma =    147 905285 933934 490801 739062 831597 514902 659513 292302 
        182595 675127 417705 095702 712339 039900 934016
                                                              [Len=93]

phi =    147 568275 772045 730870 660656 103068 115714 931370 817962 
      736601 560391 309055 520335 862966 744914 944000
                                                            [Len=93]

=======================================================================


-------------                    ----------------------         page 20
89! / 89# + 1                    n = 24: prime(24) = 89 
-------------                    ---------------------- 

89! =  16507 955160 908461 081216 919262 453619 309839 666236 496541 
      854913 520707 833171 034378 509739 399912 570787 600662 729080 
      382999 756800 000000 000000 000000
                                                           [Len=137]

89# = 23768 741896 345550 770650 537601 358310
                                      [Len=35]

89! / 89# + 1 = 694523 725020 825051 446420 532149 209597 411955 
                055040 671457 338706 588955 510775 037065 953280 
                000000 000000 000001
                                                       [Len=102]

Factorization
#1: 94099 
#2: 6 218647
#3: 18 494666 981437
#4: 58 443131 174093
#5: 1489 840216 743290 665508 300119
#6: 737032 243754 315571 280907 352212 738723
                                     [Len=36]

omega = 6;  Omega = 6;  mu = +1;  tau = 64

sigma = 694531 217483 012975 969966 712428 735690 840774 686507 093707 
        428631 852834 372563 356026 843310 828454 438466 048000
                                                             [Len=102]

phi = 694516 232561 010884 497880 528005 969849 492270 547142 607000 
      819360 921525 637135 665128 270808 367104 457490 345216
                                                           [Len=102]

=======================================================================


-------------                    ----------------------         page 21
97! / 97# + 1                    n = 25: prime(25) = 97 
-------------                    ---------------------- 

97! =     96 192759 682482 119853 328425 949563 698712 343813 919172 
      976158 104477 319333 745612 481875 498805 879175 589072 651261 
      284189 679678 167647 067832 320000 000000 000000 000000
                                                           [Len=152]

97# = 2 305567 963945 518424 753102 147331 756070
                                         [Len=37]

97! / 97# + 1 =     41 721936 280667 021214 842775 197740 704647 
                938666 856859 336935 449248 035545 074425 279071 
                887258 996965 376000 000000 000000 000001
                                                       [Len=116]

Factorization
#1: 89 
#2: 647 
#3: 6449 
#4: 196 829639 
#5:    570 804377 775579 113845 140084 714923 228047 667959 084711 
    538825 242983 631969 831787 242913 416490 381542 591177
                                                          [Len=99]

omega = 5;  Omega = 5;  mu = -1;  tau = 32

sigma =     42 262484 390795 535964 385608 824561 285729 225004 300548 
        209910 025087 617481 701713 435358 941355 345731 682014 205638 
        584130 880000
                                                             [Len=116]

phi =     41 183002 663048 748699 366087 065051 230963 707944 195859 
      745484 380638 809409 292395 123488 020829 230389 455182 392152 
      590320 996352
                                                           [Len=116]

=======================================================================


---------------                  -----------------------        page 22
101! / 101# + 1                  n = 26: prime(26) = 101 
---------------                  ----------------------- 

101! =   9425 947759 838359 420851 623124 482936 749562 312794 702543 
       768327 889353 416977 599316 221476 503087 861591 808346 911623 
       490003 549599 583369 706302 603264 000000 000000 000000 000000 
                                                            [Len=160]

101# = 232 862364 358497 360900 063316 880507 363070
                                             [Len=39]

101! / 101# + 1 =     40 478622 579503 143982 640460 496848 031649 
                  430094 584524 928694 772860 444085 831207 405755 
                  545018 678855 807795 200000 000000 000000 000001
                                                         [Len=122]

Factorization
#1: 107 
#2: 55849 
#3: 149254 503023
#4:     45 383616 852383 776893 383271 999181 668387 799180 429227 
    611638 947076 007267 619009 534006 636655 641206 385330 905509
                                                         [Len=104]

omega = 4;  Omega = 4;  mu = +1;  tau = 16

sigma =     40 857659 024288 777402 572245 450856 182519 700033 868239 
        753275 000458 574292 961434 075097 260541 866282 046576 406950 
        010437 487179 232000
                                                             [Len=122]

phi =     40 099599 682140 946911 614205 695341 811686 879283 545595 
      342878 575455 874945 119753 377762 020285 405143 362661 496054 
      172339 331808 060288
                                                           [Len=122]

=======================================================================


---------------                  -----------------------        page 23
103! / 103# + 1                  n = 27: prime(27) = 103 
---------------                  ----------------------- 

103! =     99 029007 164861 804075 467152 545817 733490 901658 221144 
       924830 052805 546998 766658 416222 832141 441073 883538 492653 
       516385 977292 093222 882134 415149 891584 000000 000000 000000 
       000000
                                                            [Len=164]

103# =  23984 823528 925228 172706 521638 692258 396210
                                               [Len=41]

103! / 103# + 1 =   4128 819503 109320 686229 326970 678499 228241 
                  869647 621542 726866 831765 296754 783155 387065 
                  591905 243292 395110 400000 000000 000000 000001
                                                         [Len=124]

Factorization
#1: 281 
#2: 3319 
#3: 1 668791
#4: 4105 856767
#5: 646110 176498 902974 386727 572279 803881 142700 113371 182675 
    202263 115519 317905 465027 783917 805971 035221 955047
                                                         [Len=102]

omega = 5;  Omega = 5;  mu = -1;  tau = 32

sigma =   4144 763717 708205 414161 133929 596567 483324 785760 
        226779 966769 110657 760575 287772 515967 298881 367447 
        072017 580301 305707 130219 397120
                                                      [Len=124]

phi =   4112 884161 675768 311450 162462 605776 551124 239143 
      923991 470610 810667 232589 292582 391771 784953 632685 
      037986 452701 569579 908113 737600
                                                     [Len=124]

=======================================================================