#### Table of irregular primes less than 10000.

An odd prime p is called irregular, if it divides the numerator of a Bernoulli number B2n with 1 ≤ n ≤ (p-3)/2. See Wikipedia article.

This table was prepared using a very slow, simple BC program which uses the identity

The B2n with 1 ≤ n ≤ (p-3)/2 and which are divisible by p, are listed, together with p, for all 497 irregular primes p less than 10000.

B32 37
B44 59
B58 67
B68 101
B24 103
B22 131
B130 149
B62 B110 157
B84 233
B164 257
B100 263
B84 271
B20 283
B156 293
B88 307
B292 311
B280 347
B186 B300 353
B100 B174 379
B200 389
B382 401
B126 409
B240 421
B366 433
B196 461
B130 463
B94 B194 467
B292 B336 B338 491
B400 523
B86 541
B270 B486 547
B222 557
B52 577
B90 B92 587
B22 593
B592 607
B522 613
B20 B174 B338 617
B428 619
B80 B226 631
B236 B242 B554 647
B48 653
B224 659
B408 B502 673
B628 677
B32 683
B12 B200 691
B378 727
B290 751
B514 757
B260 761
B732 773
B220 797
B330 B628 809
B544 811
B744 821
B102 827
B66 839
B868 877
B162 881
B418 887
B520 B820 929
B156 953
B166 971
B474 1061
B888 1091
B794 1117
B348 1129
B534 B784 B968 1151
B802 1153
B262 1193
B676 1201
B784 B866 B1118 1217
B784 1229
B874 1237
B518 1279
B510 1283
B206 B824 1291
B202 B220 1297
B176 1301
B382 B852 1307
B304 1319
B466 1327
B234 1367
B266 1381
B358 1409
B996 1429
B574 1439
B224 1483
B94 1499
B1310 1523
B862 1559
B842 1597
B1356 1609
B172 1613
B560 1619
B980 1621
B718 1637
B270 B1508 1663
B388 B1086 1669
B30 1721
B810 B942 1733
B712 1753
B1520 1759
B1192 1777
B1606 1787
B848 B1442 1789
B550 B698 B1520 1811
B1274 1831
B954 B1016 B1558 1847
B1794 1871
B1026 1877
B1260 1879
B242 1889
B1722 1901
B1058 B1320 1933
B1656 1951
B148 1979
B510 1987
B912 1993
B772 B1888 1997
B60 B600 2003
B1204 2017
B1300 2039
B1932 2053
B376 B1298 2087
B1230 2099
B1038 2111
B1624 2137
B1916 2143
B1832 2153
B154 2213
B1826 2239
B2234 2267
B876 B2166 2273
B2040 2293
B1660 B1772 2309
B2204 2357
B242 B2274 2371
B1226 2377
B2060 2381
B842 B2278 2383
B776 2389
B2126 2411
B290 B884 2423
B366 B1750 2441
B1044 2503
B2374 2543
B1464 2557
B1730 2579
B854 B2574 2591
B1772 2621
B1416 2633
B1172 2647
B710 2657
B1244 2663
B404 B2394 2671
B926 2689
B482 2753
B2528 2767
B1600 2777
B1984 B2154 2789
B2554 2791
B1832 2833
B98 2857
B352 2861
B400 B950 2909
B242 2927
B332 B1102 B2748 2939
B138 B788 2957
B776 2999
B1496 3011
B2020 3023
B700 3049
B2522 3061
B1450 3083
B1706 3089
B1704 3119
B3142 3181
B2368 3203
B98 3221
B1634 3229
B922 3257
B2222 3313
B3292 3323
B1378 3329
B2232 B2534 3391
B2076 B2558 3407
B1300 3433
B1174 3469
B2544 3491
B1416 B1724 3511
B1836 B2586 3517
B3490 3529
B2314 B3136 3533
B2082 B2130 3539
B344 B1592 3559
B1466 3581
B1922 3583
B360 B642 3593
B1976 3607
B2082 3613
B16 B2856 3617
B1104 3631
B2526 B3202 3637
B1580 3671
B2238 3677
B1884 3697
B2362 3779
B1256 3797
B3296 3821
B1840 B1998 B3286 3833
B216 B404 3851
B748 3853
B1686 B2138 3881
B1490 3917
B106 3967
B1936 3989
B534 4001
B82 B142 B2610 4003
B3228 4021
B2332 4027
B1854 4049
B3548 4051
B3620 4073
B1784 4129
B658 B2322 4157
B4190 4219
B2712 B4146 4243
B3580 B3726 4259
B2068 4261
B214 4339
B2052 4349
B636 B672 4409
B3768 4421
B2896 B2978 4451
B444 4457
B746 4493
B848 4519
B456 4523
B436 4561
B2292 B3596 4591
B3618 4637
B3226 4639
B1578 B2416 B4110 4657
B216 B4278 4663
B3592 4679
B3450 4691
B3768 4751
B252 4783
B2636 4793
B2620 4813
B4678 4861
B2924 4889
B3106 4903
B1462 4909
B492 4943
B1914 B2468 B3890 4951
B3812 4957
B1940 4969
B4208 4973
B1544 B4956 5009
B594 5039
B3092 5077
B3016 5081
B1378 5099
B190 5101
B4872 5107
B4086 5119
B4112 5167
B4732 5179
B1102 5189
B644 B2928 5209
B308 5227
B3466 5231
B4810 5297
B4156 5303
B158 5309
B1948 5351
B1482 5399
B1702 5413
B4726 5441
B1710 5443
B1150 5477
B1826 B4802 5479
B666 5501
B5206 5527
B3438 5531
B3196 5557
B938 5569
B2032 5573
B2672 5639
B4580 B5258 5641
B2218 B2680 5669
B348 5689
B2450 5701
B2200 5783
B1258 5791
B4284 5813
B1150 5821
B2308 5839
B3554 5861
B2996 5897
B3970 B5000 5903
B4240 5923
B3642 5927
B342 B5014 5939
B3274 5953
B912 6007
B5870 6011
B3396 6037
B1226 6043
B702 6091
B2008 6101
B5008 B5894 6173
B4186 6217
B1492 B3474 6247
B4272 6257
B3286 B4226 6263
B4452 B5034 6287
B2354 6317
B5102 6329
B1956 6337
B750 B5820 6343
B1190 6367
B2838 B4226 6373
B218 6379
B438 6421
B4884 B5830 6449
B3236 6451
B346 6491
B236 6521
B1564 6529
B734 6547
B1692 B1776 6569
B1744 6571
B1312 6577
B1952 B3170 6619
B2950 B4014 6659
B5252 6689
B5484 6701
B1690 6733
B4144 B6218 B6230 6763
B3994 6779
B2686 6793
B4952 6823
B4108 6827
B2254 B5144 6833
B6676 6857
B6406 6863
B2432 6949
B2010 6971
B1746 6997
B4842 7001
B1454 7039
B4154 B4972 7057
B1478 B2570 7069
B290 7109
B1502 7121
B6798 7127
B962 7177
B3906 7187
B1670 B5774 7207
B898 7211
B1436 B6930 7213
B6236 7229
B324 7309
B348 7321
B1466 7351
B4712 7411
B5286 7459
B2500 7487
B4250 7489
B3642 7499
B6924 7507
B2264 7537
B5644 7547
B116 7559
B2620 7591
B3594 7607
B5026 7643
B368 7681
B1246 B3216 B6516 7687
B2218 7691
B950 B3756 7727
B7346 7817
B3298 7823
B1392 7829
B3494 7853
B2472 B4286 7901
B584 7907
B3888 7919
B6448 7927
B3980 7937
B2506 B3436 7949
B4328 7951
B4748 7963
B622 8011
B6636 8039
B874 8059
B5354 8069
B5558 8087
B44 B3906 8089
B5968 B7898 8101
B5906 8123
B2424 B2758 8161
B5354 8179
B7680 8191
B8056 8209
B5014 8219
B4900 8221
B4806 8231
B5784 8293
B7172 8317
B7398 B8348 8369
B174 B2658 8419
B2478 8429
B1894 8443
B1300 8447
B2368 8467
B2442 8527
B6806 B7190 8537
B3562 8573
B2846 8597
B482 8599
B6070 B6778 8609
B4592 8623
B1206 8627
B3170 8629
B3944 8641
B5700 8647
B1698 8663
B2904 8669
B2658 B6794 8677
B5744 8689
B6432 8719
B6654 B7274 8731
B2688 8747
B1050 B4784 8753
B1072 8779
B2358 8821
B1552 B2620 B3830 8831
B4212 B4374 8837
B5584 8839
B6638 8849
B5336 8893
B2382 B5614 8923
B4126 8929
B4442 8933
B7404 8951
B572 8999
B4052 B4294 B5444 9011
B8214 9013
B4972 9041
B6204 9043
B8100 9059
B8996 9103
B3498 B9104 9133
B5160 B5396 9137
B1964 9199
B4802 B8470 9221
B2422 9277
B9300 9311
B1512 B7226 9323
B5726 9337
B28 9349
B1596 B2118 9377
B6674 9413
B2766 B3920 9431
B178 B9026 9433
B3760 9463
B1598 9467
B6156 9473
B1132 9511
B3122 9533
B1060 B9172 9539
B4830 9613
B860 9631
B7094 9677
B3068 B5280 9689
B138 9733
B3374 9739
B152 9743
B2410 B4586 9767
B7318 9791
B3562 9803
B1366 9811
B4562 B7548 9829
B4234 9833
B4844 9839
B1514 B3812 9859
B2980 9871
B9622 9883
B8550 9901
B5968 9907
B938 9923
B4810 B9112 9949

Keith Matthews, 27th February 2014