Bảng này gồm danh sách 1000 số nguyên tố đầu tiên và một số danh sách các số nguyên tố đặc biệt.
Đây là danh sách một nghìn số nguyên tố đầu tiên.
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1–20 | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 |
21–40 | 73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 | 127 | 131 | 137 | 139 | 149 | 151 | 157 | 163 | 167 | 173 |
41–60 | 179 | 181 | 191 | 193 | 197 | 199 | 211 | 223 | 227 | 229 | 233 | 239 | 241 | 251 | 257 | 263 | 269 | 271 | 277 | 281 |
61–80 | 283 | 293 | 307 | 311 | 313 | 317 | 331 | 337 | 347 | 349 | 353 | 359 | 367 | 373 | 379 | 383 | 389 | 397 | 401 | 409 |
81–100 | 419 | 421 | 431 | 433 | 439 | 443 | 449 | 457 | 461 | 463 | 467 | 479 | 487 | 491 | 499 | 503 | 509 | 521 | 523 | 541 |
101–120 | 547 | 557 | 563 | 569 | 571 | 577 | 587 | 593 | 599 | 601 | 607 | 613 | 617 | 619 | 631 | 641 | 643 | 647 | 653 | 659 |
121–140 | 661 | 673 | 677 | 683 | 691 | 701 | 709 | 719 | 727 | 733 | 739 | 743 | 751 | 757 | 761 | 769 | 773 | 787 | 797 | 809 |
141–160 | 811 | 821 | 823 | 827 | 829 | 839 | 853 | 857 | 859 | 863 | 877 | 881 | 883 | 887 | 907 | 911 | 919 | 929 | 937 | 941 |
161–180 | 947 | 953 | 967 | 971 | 977 | 983 | 991 | 997 | 1009 | 1013 | 1019 | 1021 | 1031 | 1033 | 1039 | 1049 | 1051 | 1061 | 1063 | 1069 |
181–200 | 1087 | 1091 | 1093 | 1097 | 1103 | 1109 | 1117 | 1123 | 1129 | 1151 | 1153 | 1163 | 1171 | 1181 | 1187 | 1193 | 1201 | 1213 | 1217 | 1223 |
201–220 | 1229 | 1231 | 1237 | 1249 | 1259 | 1277 | 1279 | 1283 | 1289 | 1291 | 1297 | 1301 | 1303 | 1307 | 1319 | 1321 | 1327 | 1361 | 1367 | 1373 |
221–240 | 1381 | 1399 | 1409 | 1423 | 1427 | 1429 | 1433 | 1439 | 1447 | 1451 | 1453 | 1459 | 1471 | 1481 | 1483 | 1487 | 1489 | 1493 | 1499 | 1511 |
241–260 | 1523 | 1531 | 1543 | 1549 | 1553 | 1559 | 1567 | 1571 | 1579 | 1583 | 1597 | 1601 | 1607 | 1609 | 1613 | 1619 | 1621 | 1627 | 1637 | 1657 |
261–280 | 1663 | 1667 | 1669 | 1693 | 1697 | 1699 | 1709 | 1721 | 1723 | 1733 | 1741 | 1747 | 1753 | 1759 | 1777 | 1783 | 1787 | 1789 | 1801 | 1811 |
281–300 | 1823 | 1831 | 1847 | 1861 | 1867 | 1871 | 1873 | 1877 | 1879 | 1889 | 1901 | 1907 | 1913 | 1931 | 1933 | 1949 | 1951 | 1973 | 1979 | 1987 |
301–320 | 1993 | 1997 | 1999 | 2003 | 2011 | 2017 | 2027 | 2029 | 2039 | 2053 | 2063 | 2069 | 2081 | 2083 | 2087 | 2089 | 2099 | 2111 | 2113 | 2129 |
321–340 | 2131 | 2137 | 2141 | 2143 | 2153 | 2161 | 2179 | 2203 | 2207 | 2213 | 2221 | 2237 | 2239 | 2243 | 2251 | 2267 | 2269 | 2273 | 2281 | 2287 |
341–360 | 2293 | 2297 | 2309 | 2311 | 2333 | 2339 | 2341 | 2347 | 2351 | 2357 | 2371 | 2377 | 2381 | 2383 | 2389 | 2393 | 2399 | 2411 | 2417 | 2423 |
361–380 | 2437 | 2441 | 2447 | 2459 | 2467 | 2473 | 2477 | 2503 | 2521 | 2531 | 2539 | 2543 | 2549 | 2551 | 2557 | 2579 | 2591 | 2593 | 2609 | 2617 |
381–400 | 2621 | 2633 | 2647 | 2657 | 2659 | 2663 | 2671 | 2677 | 2683 | 2687 | 2689 | 2693 | 2699 | 2707 | 2711 | 2713 | 2719 | 2729 | 2731 | 2741 |
401–420 | 2749 | 2753 | 2767 | 2777 | 2789 | 2791 | 2797 | 2801 | 2803 | 2819 | 2833 | 2837 | 2843 | 2851 | 2857 | 2861 | 2879 | 2887 | 2897 | 2903 |
421–440 | 2909 | 2917 | 2927 | 2939 | 2953 | 2957 | 2963 | 2969 | 2971 | 2999 | 3001 | 3011 | 3019 | 3023 | 3037 | 3041 | 3049 | 3061 | 3067 | 3079 |
441–460 | 3083 | 3089 | 3109 | 3119 | 3121 | 3137 | 3163 | 3167 | 3169 | 3181 | 3187 | 3191 | 3203 | 3209 | 3217 | 3221 | 3229 | 3251 | 3253 | 3257 |
461–480 | 3259 | 3271 | 3299 | 3301 | 3307 | 3313 | 3319 | 3323 | 3329 | 3331 | 3343 | 3347 | 3359 | 3361 | 3371 | 3373 | 3389 | 3391 | 3407 | 3413 |
481–500 | 3433 | 3449 | 3457 | 3461 | 3463 | 3467 | 3469 | 3491 | 3499 | 3511 | 3517 | 3527 | 3529 | 3533 | 3539 | 3541 | 3547 | 3557 | 3559 | 3571 |
501–520 | 3581 | 3583 | 3593 | 3607 | 3613 | 3617 | 3623 | 3631 | 3637 | 3643 | 3659 | 3671 | 3673 | 3677 | 3691 | 3697 | 3701 | 3709 | 3719 | 3727 |
521–540 | 3733 | 3739 | 3761 | 3767 | 3769 | 3779 | 3793 | 3797 | 3803 | 3821 | 3823 | 3833 | 3847 | 3851 | 3853 | 3863 | 3877 | 3881 | 3889 | 3907 |
541–560 | 3911 | 3917 | 3919 | 3923 | 3929 | 3931 | 3943 | 3947 | 3967 | 3989 | 4001 | 4003 | 4007 | 4013 | 4019 | 4021 | 4027 | 4049 | 4051 | 4057 |
561–580 | 4073 | 4079 | 4091 | 4093 | 4099 | 4111 | 4127 | 4129 | 4133 | 4139 | 4153 | 4157 | 4159 | 4177 | 4201 | 4211 | 4217 | 4219 | 4229 | 4231 |
581–600 | 4241 | 4243 | 4253 | 4259 | 4261 | 4271 | 4273 | 4283 | 4289 | 4297 | 4327 | 4337 | 4339 | 4349 | 4357 | 4363 | 4373 | 4391 | 4397 | 4409 |
601–620 | 4421 | 4423 | 4441 | 4447 | 4451 | 4457 | 4463 | 4481 | 4483 | 4493 | 4507 | 4513 | 4517 | 4519 | 4523 | 4547 | 4549 | 4561 | 4567 | 4583 |
621–640 | 4591 | 4597 | 4603 | 4621 | 4637 | 4639 | 4643 | 4649 | 4651 | 4657 | 4663 | 4673 | 4679 | 4691 | 4703 | 4721 | 4723 | 4729 | 4733 | 4751 |
641–660 | 4759 | 4783 | 4787 | 4789 | 4793 | 4799 | 4801 | 4813 | 4817 | 4831 | 4861 | 4871 | 4877 | 4889 | 4903 | 4909 | 4919 | 4931 | 4933 | 4937 |
661–680 | 4943 | 4951 | 4957 | 4967 | 4969 | 4973 | 4987 | 4993 | 4999 | 5003 | 5009 | 5011 | 5021 | 5023 | 5039 | 5051 | 5059 | 5077 | 5081 | 5087 |
681–700 | 5099 | 5101 | 5107 | 5113 | 5119 | 5147 | 5153 | 5167 | 5171 | 5179 | 5189 | 5197 | 5209 | 5227 | 5231 | 5233 | 5237 | 5261 | 5273 | 5279 |
701–720 | 5281 | 5297 | 5303 | 5309 | 5323 | 5333 | 5347 | 5351 | 5381 | 5387 | 5393 | 5399 | 5407 | 5413 | 5417 | 5419 | 5431 | 5437 | 5441 | 5443 |
721–740 | 5449 | 5471 | 5477 | 5479 | 5483 | 5501 | 5503 | 5507 | 5519 | 5521 | 5527 | 5531 | 5557 | 5563 | 5569 | 5573 | 5581 | 5591 | 5623 | 5639 |
741–760 | 5641 | 5647 | 5651 | 5653 | 5657 | 5659 | 5669 | 5683 | 5689 | 5693 | 5701 | 5711 | 5717 | 5737 | 5741 | 5743 | 5749 | 5779 | 5783 | 5791 |
761–780 | 5801 | 5807 | 5813 | 5821 | 5827 | 5839 | 5843 | 5849 | 5851 | 5857 | 5861 | 5867 | 5869 | 5879 | 5881 | 5897 | 5903 | 5923 | 5927 | 5939 |
781–800 | 5953 | 5981 | 5987 | 6007 | 6011 | 6029 | 6037 | 6043 | 6047 | 6053 | 6067 | 6073 | 6079 | 6089 | 6091 | 6101 | 6113 | 6121 | 6131 | 6133 |
801–820 | 6143 | 6151 | 6163 | 6173 | 6197 | 6199 | 6203 | 6211 | 6217 | 6221 | 6229 | 6247 | 6257 | 6263 | 6269 | 6271 | 6277 | 6287 | 6299 | 6301 |
821–840 | 6311 | 6317 | 6323 | 6329 | 6337 | 6343 | 6353 | 6359 | 6361 | 6367 | 6373 | 6379 | 6389 | 6397 | 6421 | 6427 | 6449 | 6451 | 6469 | 6473 |
841–860 | 6481 | 6491 | 6521 | 6529 | 6547 | 6551 | 6553 | 6563 | 6569 | 6571 | 6577 | 6581 | 6599 | 6607 | 6619 | 6637 | 6653 | 6659 | 6661 | 6673 |
861–880 | 6679 | 6689 | 6691 | 6701 | 6703 | 6709 | 6719 | 6733 | 6737 | 6761 | 6763 | 6779 | 6781 | 6791 | 6793 | 6803 | 6823 | 6827 | 6829 | 6833 |
881–900 | 6841 | 6857 | 6863 | 6869 | 6871 | 6883 | 6899 | 6907 | 6911 | 6917 | 6947 | 6949 | 6959 | 6961 | 6967 | 6971 | 6977 | 6983 | 6991 | 6997 |
901–920 | 7001 | 7013 | 7019 | 7027 | 7039 | 7043 | 7057 | 7069 | 7079 | 7103 | 7109 | 7121 | 7127 | 7129 | 7151 | 7159 | 7177 | 7187 | 7193 | 7207 |
921–940 | 7211 | 7213 | 7219 | 7229 | 7237 | 7243 | 7247 | 7253 | 7283 | 7297 | 7307 | 7309 | 7321 | 7331 | 7333 | 7349 | 7351 | 7369 | 7393 | 7411 |
941–960 | 7417 | 7433 | 7451 | 7457 | 7459 | 7477 | 7481 | 7487 | 7489 | 7499 | 7507 | 7517 | 7523 | 7529 | 7537 | 7541 | 7547 | 7549 | 7559 | 7561 |
961–980 | 7573 | 7577 | 7583 | 7589 | 7591 | 7603 | 7607 | 7621 | 7639 | 7643 | 7649 | 7669 | 7673 | 7681 | 7687 | 7691 | 7699 | 7703 | 7717 | 7723 |
981–1000 | 7727 | 7741 | 7753 | 7757 | 7759 | 7789 | 7793 | 7817 | 7823 | 7829 | 7841 | 7853 | 7867 | 7873 | 7877 | 7879 | 7883 | 7901 | 7907 | 7919 |
2, 5, 877, 27 644 437, 35 742 549 198 872 617 291 353 508 656 626 642 567, 359 334 085 968 622 831 041 960 188 598 043 661 065 388 726 959 079 837
11, 31, 61, 101, 151, 211, 281, 661, 911, 1 051, 1 201, 1 361
43, 71, 197, 463, 547, 953, 1 471, 1 933, 2 647, 2 8 432 003
5, 13, 41, 61, 113, 181, 313, 421, 613, 761
19, 31, 109, 199, 223, 409, 571, 631, 829, 1 489, 1 999, 2 972
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 167, 173, 179, 181, 191, 193, 199 , 203, 207, 211, 227, 233, 239, 251, 257, 263, 269, 281, 293, 307, 311, 317, 337, 347, 353, 359, 379, 389, 401, 409, 419, 431, 443, 449, 461, 467, 479, 487, 491, 499, 503
(3, 7), (7, 11), (13, 17), (19, 23), (37, 41), (43, 47), (67, 71), (79, 83), (97, 101), (103, 107), (109, 113), (127, 131), (163, 167), (193, 197), (223, 227), (229, 233), (277, 281), (307, 311), (313, 317), (349, 353), (379, 383), (397, 401), (439, 441), (457, 461), (487, 491), (499, 503), (613, 617), (643, 647), (673, 677), (739, 743), (757, 761), (769, 773), (823, 827), (853, 857), (859, 863), (877, 881), (883, 887), (907, 911), (937, 941), (967, 971), (1009, 1013), (1087, 1091)
Các số nguyên tố khối có dạng (x3 − y3) / (x − y), x = y + 1:
Các số nguyên tố khối dạng (x3 − y3) / (x − y), x = y + 2:
3, 393 050 634 124 102 232 869 567 034 555 427 371 542 904 833
7, 13, 19, 31, 37, 43, 61, 67, 73, 79,97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463, 487, 499.
Tới tháng 8/2005, mới chỉ biết các số nguyên tố Mersenne kép.
7, 127, 2 147 483 647, 170 141 183 460 469 231 731 687 303 715 884 105 727
2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401, 419, 431, 443, 449, 461, 467, 479, 491
3, 7, 31, 211, 2 311
2, 3, 5, 7, 23, 719, 5 039, 39 916 801, 479 001 599, 87 178 291 199, 10 888 869 450 418 352 160 768 000 001, 265 252 859 812 191 058 636 308 479 999 999, 263 130 836 933 693 530 167 218 012 159 999 999, 8 683 317 618 811 886 495 518 194 401 279 999 999
Đến tháng 9-2005, mới chỉ biết các số nguyên tố Fermat.
3, 5, 17, 257, 65 537
2, 3, 5, 13, 89, 233, 1 597, 28 657, 514 229, 433 494 437, 2 971 215 073
3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107, 127, 131, 139, 151, 163, 167, 179, 191, 199, 211, 223, 227, 239, 251, 263, 271, 283, 307, 311, 331, 347, 359, 367, 379, 383, 419, 431, 439, 443, 463, 467, 479, 487, 491, 499
17
7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379, 383, 397, 409, 487, 563
2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 101, 107, 109, 127, 131, 139, 149, 151, 157, 167, 173, 179, 181, 191, 197, 199, 211, 223, 229, 233, 251, 263, 269, 271, 277, 281, 283, 293, 311, 313, 317, 331, 347, 349, 359,
23, 47, 59, 83, 89, 113, 167, 269, 389, 419, 509, 659, 839
37, 59, 67, 101, 103, 131, 149, 157, 233, 257, 263, 271, 283, 293, 307, 311, 347, 353, 379, 389, 401, 409, 421, 433, 461, 463, 467, 491
7, 23, 79, 1087, 66047, 263167, 16785407, 1073807359
7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, 149, 167, 179, 181, 193, 223, 229, 233, 257, 263, 269, 313, 337, 367, 379, 383, 389, 419, 433, 461, 487, 491, 499
2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349
3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193, 211, 223, 241, 283, 307, 331, 349, 367, 409, 421, 433, 463, 487, 541, 577, 601, 613, 619, 631, 643, 673, 727, 739, 769, 787, 823, 883, 937, 991, 997, 1009, 1021, 1039, 1087, 1093, 1117, 1123, 1201, 1231, 1249, 1291, 1303, 1459, 1471, 1543, 1567, 1579, 1597, 1663, 1693, 1723, 1777, 1801, 1831, 1879, 1933, 1987, 2053, 2083, 2113, 2221, 2239, 2251, 2281, 2311, 2467, 2473, 2557, 2593, 2647, 2671, 2689, 2797, 2851, 2887, 2953, 2971, 3037, 3049, 3109, 3121, 3163, 3187, 3229, 3259, 3301, 3307, 3313
2, 5, 13, 29, 89, 233, 433, 1 597, 2 897
13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Tính đến tháng 12 năm 2021[cập nhật] có 51 số nguyên tố Mersenne 2p − 1 tương ứng với số mũ p dưới đây:
2, 127, 15 511, 953 467 954 114 363
7, 41, 239, 9369319, 63018038201, 489133282872437279, 19175002942688032928599
2, 3, 5, 7, 37, 151, 3329, 23833
2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741, 15451, 15551, 16061, 16361, 16561, 16661, 17471, 17971, 18181, 18481, 19391, 19891, 19991, 30103, 30203, 30403, 30703, 30803, 31013, 31513, 32323, 32423, 33533, 34543, 34843, 35053, 35753, 36263, 36563, 37273, 37573, 38083, 38183, 38783, 39293, 70207, 70507, 70607, 71317, 71917, 72227, 72727, 73037, 73237, 73637, 74047, 74747, 75557, 76367, 76667, 77377, 77477, 77977, 78487, 78787, 78887, 79397, 79697, 79997, 90709, 91019, 93139, 93239, 93739, 94049, 94349, 94649, 94849, 94949, 95959, 96269, 96469, 96769, 97379, 97579, 97879, 98389, 98689
2, 5, 29, 5741, 33461
2, 3, 5, 7, 17, 29, 277, 367, 853
2, 3, 5, 7, 13, 17, 19, 37, 73, 97, 109, 163, 193, 257, 433, 487, 577, 769, 1153, 1297, 1459, 2593, 2917, 3457, 3889, 10369, 12289, 17497, 18433, 39367, 52489, 65537, 139969, 147457, 209953, 331777, 472393, 629857, 746497, 786433, 839809, 995329
(5, 7, 11, 13), (11, 13, 17, 19), (101, 103, 107, 109), (191, 193, 197, 199), (821, 823, 827, 829), (1481, 1483, 1487, 1489), (1871, 1873, 1877, 1879), (2081, 2083, 2087, 2089), (3251, 3253, 3257, 3259), (3461, 3463, 3467, 3469),(5651, 5653, 5657, 5659), (9431, 9433, 9437, 9439), (13001, 13003, 13007, 13009), (15641, 15643, 15647, 15649), (15731, 15733, 15737, 15739), (16061, 16063, 16067, 16069), (18041, 18043, 18047, 18049), (18911, 18913, 18917, 18919), (19421, 19423, 19427, 19429), (21011, 21013, 21017, 21019), (22271, 22273, 22277, 22279), (25301, 25303, 25307, 25309), (31721, 31723, 31727, 31729), (34841, 34843, 34847, 34849), (43781, 43783, 43787, 43789), (51341, 51343, 51347, 51349), (55331, 55333, 55337, 55339), (62981, 62983, 62987, 62989), (67211, 67213, 67217, 67219), (69491, 69493, 69497, 69499), (72221, 72223, 72227, 72229), (77261, 77263, 77267, 77269), (79691, 79693, 79697, 79699), (81041, 81043, 81047, 81049), (82721, 82723, 82727, 82729), (88811, 88813, 88817, 88819), (97841, 97843, 97847, 97849), (99131, 99133, 99137, 99139)
(5, 7, 11), (7, 11, 13), (11, 13, 17), (13, 17, 19), (17, 19, 23), (37, 41, 43), (41, 43, 47), (67, 71, 73), (97, 101, 103), (101, 103, 107), (103, 107, 109), (107, 109, 113), (191, 193, 197), (193, 197, 199), (223, 227, 229), (227, 229, 233), (277, 281, 283), (307, 311, 313), (311, 313, 317), (347, 349, 353), (457, 461, 463), (461, 463, 467), (613, 617, 619), (641, 643, 647), (821, 823, 827), (823, 827, 829), (853, 857, 859), (857, 859, 863), (877, 881, 883), (881, 883, 887)
5, 7, 29, 31, 211, 2309, 2311, 30029
5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 293, 313, 317, 337, 349, 353, 373, 389, 397, 401, 409, 421, 433, 449, 457, 461
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47, 53, 61, 71, 73, 79, 83, 89, 97, 107, 109, 113, 127, 137, 139, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 239, 241, 251, 269, 277, 281, 313, 317, 331, 337, 349, 359, 367, 373, 383, 397, 401
1
5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907
3, 5, 7, 31, 53, 97, 211, 233, 277, 367, 389, 457, 479
(5,11), (7,13), (11,17), (13,19), (17,23), (23,29), (31,37), (37,43), (41,47), (47,53), (53,59), (61,67), (67,73), (73,79), (83,89), (97.103), (101.107), (103.109), (107.113), (131.137), (151.157), (157.163), (167.173), (173.179), (191.197), (193.199), (223.229), (227.233), (233.239), (251.257), (263.269), (271.277), (277.283), (307.313), (311.317), (331.337), (347.353), (353.359), (367.373), (373.379), (383.389), (433.439), (443.449), (457.463), (461.467), (503.509)
2, 23, 2357
Số nguyên tố Smarandache-Wellin thứ tư có khoảng 355 chữ số.
2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 593, 641, 653, 659, 683, 719, 743, 761, 809, 911, 953, 1013, 1019, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1439, 1451, 1481, 1499, 1511,1559
13, 37, 73, 181, 337, 433, 541, 661, 937, 1093, 2053, 2281, 2521, 3037, 3313
Đến tháng 10-2006, mới chỉ biết các số nguyên tố Stern sau, và có khả năng chỉ có chúng.
2, 3, 17, 137, 227, 977, 1187, 1493
Có 15 số nguyên tố supersingular.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71
2, 5, 11, 23, 47, 191, 383, 6143
(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), (149, 151), (179, 181), (191, 193), (197, 199), (227, 229), (239, 241), (269, 271), (281, 283), (311, 313), (347, 349), (419, 421), (431, 433), (461, 463), (521, 523), (569, 571), (599, 601), (617, 619), (641, 643), (659, 661), (809, 811), (821, 823), (827, 829), (857, 859), (881, 883), (1019, 1021), (1031, 1033), (1049, 1051), (1061, 1063), (1091, 1093), (1151, 1153), (1229, 1231), (1277, 1279), (1289, 1291), (1301, 1303), (1319, 1321), (1427, 1429), (1451, 1453), (1481, 1483), (1487, 1489), (1607, 1609), (1619, 1621), (1667, 1669), (1697, 1699), (1721, 1723), (1787, 1789), (1871, 1873), (1877, 1879), (1931, 1933), (1949, 1951), (1997, 1999), (2027, 2029), (2081, 2083), (2087, 2089), (2111, 2113), (2129, 2131), (2141, 2143), (2237, 2239), (2267, 2269), (2309, 2311), (2339, 2341), (2381, 2383), (2549, 2551), (2591, 2593), (2687, 2689), (2711, 2713), (2789, 2791), (2801, 2803), (2999, 3001)
3, 11, 37, 101, 9091, 9901, 333667
3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167, 191, 199, 313, 347, 701, 1709, 2617, 3539, 5807, 10501, 10691, 11279, 12391, 14479, 42737, 83339, 95369, 117239, 127031, 138937, 141079, 267017, 269987, 374321
2, 3, 11, 23, 983, 2179, 24631, 3626149
Đến tháng 9 năm 2005 mới chỉ biết các nguyên tố Wieferich sau:
1093, 3511
Đến tháng 9 năm 2005, mới chỉ biết các số nguyên tố Wilson sau:
5, 13, 563
Đến tháng 9 năm 2005, mới chỉ biết các số nguyên tố Wolstenholme:
16843, 2124679
3, 7, 23, 383, 32212254719, 2833419889721787128217599
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