Ini adalah daftar dinamis, yang mungkin tidak dapat memuaskan standar tertentu untuk kelengkapan. Anda dapat membantu dengan mengembangkannya dengan menambahkan klaim yang diberikan sumber tepercaya.
Bilangan prima adalah bilangan asli lebih besar dari 1 yang tidak memiliki pembagi positif selain 1 dan dirinya sendiri. Menurut Teorema Euklides, ada bilangan prima yang takhingga. Himpunan bagian dari bilangan prima dapat dibuat dengan berbagai rumus untuk bilangan prima. 1000 bilangan prima pertama tercantum di bawah ini, diikuti dengan daftar jenis bilangan prima yang terkenal dalam urutan abjad, memberikan suku pertamanya masing-masing. 1 bukan bilangan prima atau komposit.

1000 bilangan prima pertama
---------------------------

Tabel berikut mencantumkan 1000 bilangan prima pertama, dengan 20 kolom bilangan prima berurutan di masing-masing dari 50 baris.

|  | 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 | angka | 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 |

(barisan A000040 pada OEIS).

Proyek verifikasi konjektur Goldbach melaporkan bahwa mereka telah menghitung semua bilangan prima di bawah ini 4×1018. That means 95,676,260,903,887,607 primes (nearly 1017), tapi mereka tidak disimpan. Ada rumus yang diketahui untuk mengevaluasi fungsi penghitungan bilangan prima (jumlah bilangan prima di bawah nilai yang diberikan) lebih cepat daripada menghitung bilangan prima. Ini telah digunakan untuk menghitung bahwa ada 1.925.320.391.606.803.968.923 bilangan prima (kira-kira 2×1021) di bawah 1023. Perhitungan yang berbeda menemukan bahwa ada 18.435.599.767.349.200.867.866 bilangan prima (kira-kira 2×1022) di bawah 1024, bila hipotesis Riemann benar.

Daftar bilangan prima menurut tipe
----------------------------------

 
Di bawah ini terdaftar bilangan prima pertama dari banyak bentuk dan tipe bernama. Lebih jelasnya ada di artikel untuk namanya. {\displaystyle n} adalah bilangan asli (termasuk 0) di definisikan

### Bilangan prima Bell

Bilangan prima yang merupakan bilangan partisi himpunan dengan {\displaystyle n} anggota.

2, 5, 877, 27644437, 35742549198872617291353508656626642567, 359334085968622831041960188598043661065388726959079837.

Suku selanjutnya memiliki 6539 digit. (OEIS A051131)

### Bilangan prima berimbang

Bentuk: {\displaystyle p-n,\,p,\,p+n}

5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103, 1123, 1187, 1223, 1367, 1511, 1747, 1753, 1907, 2287, 2417, 2677, 2903, 2963, 3307, 3313, 3637, 3733, 4013, 4409, 4457, 4597, 4657, 4691, 4993, 5107, 5113, 5303, 5387, 5393 (barisan A006562 dalam OEIS).

### Bilangan prima Carol

Dari bentuk {\displaystyle (2^{n}-1)^{2}-2}

7, 47, 223, 3967, 16127, 1046527, 16769023, 1073676287, 68718952447, 274876858367, 4398042316799, 1125899839733759, 18014398241046527, 1298074214633706835075030044377087 (OEIS A091516)

### Bilangan prima Chen

Dimana {\displaystyle p} adalah bilangan prima dan {\displaystyle p+2} adalah baik bilangan prima maupun semiprima.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, 107, 109, 113, 127, 131, 137, 139, 149, 157, 167, 179, 181, 191, 197, 199, 211, 227, 233, 239, 251, 257, 263, 269, 281, 293, 307, 311, 317, 337, 347, 353, 359, 379, 389, 401, 409 (OEIS A109611)

### Bilangan prima Cuban

Dari bentuk {\displaystyle {\frac {x^{3}-y^{3}}{x-y}}} dimana {\displaystyle x=y+1}.

7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919, 1657, 1801, 1951, 2269, 2437, 2791, 3169, 3571, 4219, 4447, 5167, 5419, 6211, 7057, 7351, 8269, 9241, 10267, 11719, 12097, 13267, 13669, 16651, 19441, 19927, 22447, 23497, 24571, 25117, 26227, 27361, 33391, 35317 (OEIS A002407)

Dari bentuk {\displaystyle {\frac {x^{3}-y^{3}}{x-y}}} dimana {\displaystyle x=y+2}.

13, 109, 193, 433, 769, 1201, 1453, 2029, 3469, 3889, 4801, 10093, 12289, 13873, 18253, 20173, 21169, 22189, 28813, 37633, 43201, 47629, 60493, 63949, 65713, 69313, 73009, 76801, 84673, 106033, 108301, 112909, 115249 (OEIS A002648)

### Bilangan prima Cullen

Dari bentuk {\displaystyle n\cdot 2^{n}+1}.

3, 393050634124102232869567034555427371542904833 (OEIS A050920)

### Bilangan prima dihedral

Bilangan prima yang tetap bilangan prima ketika dibaca terbalik atau tercermin dalam sebuah layar tujuh segmen.

2, 5, 11, 101, 181, 1181, 1811, 18181, 108881, 110881, 118081, 120121,
121021, 121151, 150151, 151051, 151121, 180181, 180811, 181081 (OEIS A134996)

### Bilangan prima Eisenstein tanpa bagian imajiner/khayal

Bilangan bulat Eisenstein yang merupakan bilangan taktereduksi dan bilangan real (bilangan prima dari bentuk {\displaystyle 3n-1}).

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 (OEIS A003627)

### Bilangan prima Euclid

Dari bentuk {\displaystyle p\_{n}\#+1} (sebuah himpunan bagian bilangan prima primorial).

3, 7, 31, 211, 2311, 200560490131 (OEIS A018239)

### Bilangan prima faktorial

Dari bentuk *n*! - 1 atau *n*! + 1.

2, 3, 5, 7, 23, 719, 5039, 39916801, 479001599, 87178291199, 10888869450418352160768000001, 265252859812191058636308479999999, 263130836933693530167218012159999999, 8683317618811886495518194401279999999 (OEIS A088054)

### Bilangan prima Fermat

Dari bentuk {\displaystyle 2^{2^{n}}+1}.

3, 5, 17, 257, 65537 (OEIS A019434)

Hingga Agustus 2019[update], ini hanya dikenal sebagai bilangan prima Fermat, dan secara dugaan hanyalah bilangan prima Fermat. Peluang dari keberadaan bilangan prima Fermat lainnya lebih kecil dari satu miliar.

#### Bilangan prima Fermat rampat

Dari bentuk {\displaystyle a^{2^{n}}+1} untuk bilangan bulat tetap {\displaystyle a}.

*a* = 2: 3, 5, 17, 257, 65537

*a* = 4: 5, 17, 257, 65537

*a* = 6: 7, 37, 1297

*a* = 8: (tidak ada)

*a* = 10: 11, 101

*a* = 12: 13

*a* = 14: 197

*a* = 16: 17, 257, 65537

*a* = 18: 19

*a* = 20: 401, 160001

*a* = 22: 23

*a* = 24: 577, 331777

Hingga April 2017[update], ini haya diketahui bilangan prima Fermat rampat untuk {\displaystyle a\leq 24}.

### Bilangan prima Fibonacci

Bilangan prima dalam barisan Fibonacci {\displaystyle F\_{0}=0}*,* {\displaystyle F\_{1}=1}*,* {\displaystyle F\_{n}=F\_{n-1}+F\_{n-2}}.

2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 99194853094755497, 1066340417491710595814572169, 19134702400093278081449423917 (OEIS A005478)

### Bilangan prima *fortunate*

Bilangan f*ortunate* bahwa semua bilangan prima (ini telah diduga semuanya).

3, 5, 7, 13, 17, 19, 23, 37, 47, 59, 61, 67, 71, 79, 89, 101, 103, 107, 109, 127, 151, 157, 163, 167, 191, 197, 199, 223, 229, 233, 239, 271, 277, 283, 293, 307, 311, 313, 331, 353, 373, 379, 383, 397 (OEIS A046066)

### Bilangan prima melingkar

Sebuah bilangan prima melingkar merupakan sebuah bilangan yang tetap bilangan prima pada suatu rotasi siklik mengenai digitnya (dalam basis 10).

2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 197, 199, 311, 337, 373, 719, 733, 919, 971, 991, 1193, 1931, 3119, 3779, 7793, 7937, 9311, 9377, 11939, 19391, 19937, 37199, 39119, 71993, 91193, 93719, 93911, 99371, 193939, 199933, 319993, 331999, 391939, 393919, 919393, 933199, 939193, 939391, 993319, 999331 (OEIS A068652)

Beberapa sumber hanya mencatat bilangan prima terkecil dalam setiap siklus, contohnya, mencatat 13, tetapi menghilangkan 31 (OEIS juga menyebut ini barisan bilangan prima melingkar, tetapi bukan di atas barisan):

2, 3, 5, 7, 11, 13, 17, 37, 79, 113, 197, 199, 337, 1193, 3779, 11939, 19937, 193939, 199933, 1111111111111111111, 11111111111111111111111 (OEIS A016114)

Semua bilangan prima satuan berulang adalah melingkar.

### Bilangan prima sepupu

Lihat pula: § Bilangan prima kembar, § Bilangan prima kembar tiga, dan § Bilangan prima kembar empat
Dimana {\displaystyle (p,p+4)} keduanya bilangan prima.

(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) (OEIS A023200, OEIS A046132)

### Bilangan prima takberaturan Euler

Sebuah bilangan prima {\displaystyle p} yang membagi bilangan Euler {\displaystyle E\_{2n}} untuk suatu {\displaystyle 0\leq 2n\leq p-3}.

19, 31, 43, 47, 61, 67, 71, 79, 101, 137, 139, 149, 193, 223, 241, 251, 263, 277, 307, 311, 349, 353, 359, 373, 379, 419, 433, 461, 463, 491, 509, 541, 563, 571, 577, 587 (OEIS A120337)

#### Bilangan prima takberaturan {\displaystyle (p,\,p-3)} Euler

Bilangan prima {\displaystyle p} sehingga {\displaystyle (p,p-3)} adalah sebuah pasangan takberaturan Euler.

149, 241, 2946901 (OEIS A198245)

### *Emirp*

Bilangan prima yang menjadi sebuah bilangan prima yang berbeda ketika digit desimalnya terbalik. Nama "*emirp*" diperoleh dengan membalikkan kata "*prime*" (yang berarti prima)).

13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991 (OEIS A006567)

### Gaussian primes

Prime elements of the Gaussian integers; equivalently, primes of the form 4*n* + 3.

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, 503 (OEIS A002145)

### Good primes

Primes *p**n* for which *p**n*2 > *p**n*−*i* *p**n*+*i* for all 1 ≤ *i* ≤ *n*−1, where *p**n* is the *n*th prime.

5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149, 179, 191, 223, 227, 251, 257, 269, 307 (OEIS A028388)

### Happy primes

Happy numbers that are prime.

7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379, 383, 397, 409, 487, 563, 617, 653, 673, 683, 709, 739, 761, 863, 881, 907, 937, 1009, 1033, 1039, 1093 (OEIS A035497)

### Harmonic primes

Primes *p* for which there are no solutions to *H**k* ≡ 0 (mod *p*) and *H**k* ≡ −*ω**p* (mod *p*) for 1 ≤ *k* ≤ *p*−2, where *H**k* denotes the *k*-th harmonic number and *ω**p* denotes the Wolstenholme quotient.

5, 13, 17, 23, 41, 67, 73, 79, 107, 113, 139, 149, 157, 179, 191, 193, 223, 239, 241, 251, 263, 277, 281, 293, 307, 311, 317, 331, 337, 349 (OEIS A092101)

### Higgs primes for squares

Primes *p* for which *p* − 1 divides the square of the product of all earlier terms.

2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 67, 71, 79, 101, 107, 127, 131, 139, 149, 151, 157, 173, 181, 191, 197, 199, 211, 223, 229, 263, 269, 277, 283, 311, 317, 331, 347, 349 (OEIS A007459)

### Highly cototient primes

Primes that are a cototient more often than any integer below it except 1.

2, 23, 47, 59, 83, 89, 113, 167, 269, 389, 419, 509, 659, 839, 1049, 1259, 1889 (OEIS A105440)

### Home primes

For *n* ≥ 2, write the prime factorization of n in base 10 and concatenate the factors; iterate until a prime is reached.

2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, 11, 223, 13, 13367, 1129, 31636373, 17, 233, 19, 3318308475676071413, 37, 211, 23, 331319, 773, 3251, 13367, 227, 29, 547, 31, 241271, 311, 31397, 1129, 71129, 37, 373, 313, 3314192745739, 41, 379, 43, 22815088913, 3411949, 223, 47, 6161791591356884791277 (OEIS A037274)

### Irregular primes

Odd primes *p* that divide the class number of the *p*-th cyclotomic field.

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, 523, 541, 547, 557, 577, 587, 593, 607, 613 (OEIS A000928)

#### (*p*, *p* − 3) irregular primes

(See Wolstenholme prime)

#### (*p*, *p* − 5) irregular primes

Primes *p* such that (*p*, *p*−5) is an irregular pair.

37

#### (*p*, *p* − 9) irregular primes

Primes *p* such that (*p*, *p* − 9) is an irregular pair.

67, 877 (OEIS A212557)

### Isolated primes

Primes *p* such that neither *p* − 2 nor *p* + 2 is prime.

2, 23, 37, 47, 53, 67, 79, 83, 89, 97, 113, 127, 131, 157, 163, 167, 173, 211, 223, 233, 251, 257, 263, 277, 293, 307, 317, 331, 337, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 439, 443, 449, 457, 467, 479, 487, 491, 499, 503, 509, 541, 547, 557, 563, 577, 587, 593, 607, 613, 631, 647, 653, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 839, 853, 863, 877, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 (OEIS A007510)

### Kynea primes

Of the form (2*n* + 1)2 − 2.

2, 7, 23, 79, 1087, 66047, 263167, 16785407, 1073807359, 17180131327, 68720001023, 4398050705407, 70368760954879, 18014398777917439, 18446744082299486207 (OEIS A091514)

### Leyland primes

Of the form *x**y* + *y**x*, with 1 < *x* < *y*.

17, 593, 32993, 2097593, 8589935681, 59604644783353249, 523347633027360537213687137, 43143988327398957279342419750374600193 (OEIS A094133)

### Long primes

Primes *p* for which, in a given base *b*, {\displaystyle {\frac {b^{p-1}-1}{p}}} gives a cyclic number. They are also called full reptend primes. Primes *p* for base 10:

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, 503, 509, 541, 571, 577, 593 (OEIS A001913)

### Lucas primes

Primes in the Lucas number sequence *L*0 = 2, *L*1 = 1,
*L**n* = *L**n*−1 + *L**n*−2.

2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879, 119218851371, 5600748293801, 688846502588399, 32361122672259149 (OEIS A005479)

### Lucky primes

Lucky numbers that are prime.

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 (OEIS A031157)

### Mersenne primes

Of the form 2*n* − 1.

3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727 (OEIS A000668)

Hingga 2018[update], there are 51 known Mersenne primes. The 13th, 14th, and 51st have respectively 157, 183, and 24,862,048 digits.

Hingga 2018[update], this class of prime numbers also contains the largest known prime: M82589933, the 51st known Mersenne prime.

#### Mersenne divisors

Primes *p* that divide 2*n* − 1, for some prime number n.

3, 7, 23, 31, 47, 89, 127, 167, 223, 233, 263, 359, 383, 431, 439, 479, 503, 719, 839, 863, 887, 983, 1103, 1319, 1367, 1399, 1433, 1439, 1487, 1823, 1913, 2039, 2063, 2089, 2207, 2351, 2383, 2447, 2687, 2767, 2879, 2903, 2999, 3023, 3119, 3167, 3343 (OEIS A122094)

All Mersenne primes are, by definition, members of this sequence.

#### Mersenne prime exponents

Primes *p* such that 2*p* − 1 is prime.

2, 3, 5, 7, 13, 17, 19, 31, 61, 89,

107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423,

9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049,

216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011,

24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609 (OEIS A000043)

Hingga Desember 2018[update] four more are known to be in the sequence, but it is not known whether they are the next:  

57885161, 74207281, 77232917, 82589933

#### Double Mersenne primes

A subset of Mersenne primes of the form 22*p*−1 − 1 for prime *p*.

7, 127, 2147483647, 170141183460469231731687303715884105727 (primes in OEIS A077586)

As of June 2017, these are the only known double Mersenne primes, and number theorists think these are probably the only double Mersenne primes.[*butuh rujukan*]

#### Generalized repunit primes

Of the form (*a**n* − 1) / (*a* − 1) for fixed integer *a*.

For *a* = 2, these are the Mersenne primes, while for *a* = 10 they are the repunit primes. For other small *a*, they are given below:

*a* = 3: 13, 1093, 797161, 3754733257489862401973357979128773, 6957596529882152968992225251835887181478451547013 (OEIS A076481)

*a* = 4: 5 (the only prime for *a* = 4)

*a* = 5: 31, 19531, 12207031, 305175781, 177635683940025046467781066894531, 14693679385278593849609206715278070972733319459651094018859396328480215743184089660644531 (OEIS A086122)

*a* = 6: 7, 43, 55987, 7369130657357778596659, 3546245297457217493590449191748546458005595187661976371 (OEIS A165210)

*a* = 7: 2801, 16148168401, 85053461164796801949539541639542805770666392330682673302530819774105141531698707146930307290253537320447270457

*a* = 8: 73 (the only prime for *a* = 8)

*a* = 9: none exist

#### Other generalizations and variations

Many generalizations of Mersenne primes have been defined. This include the following:

* Primes of the form *bn* − (*b* − 1)*n*, including the Mersenne primes and the cuban primes as special cases
* Williams primes, of the form (*b* − 1)·*bn* − 1

### Mills primes

Of the form ⌊θ3*n*⌋, where θ is Mills' constant. This form is prime for all positive integers *n*.

2, 11, 1361, 2521008887, 16022236204009818131831320183 (OEIS A051254)

### Minimal primes

Primes for which there is no shorter sub-sequence of the decimal digits that form a prime. There are exactly 26 minimal primes:

2, 3, 5, 7, 11, 19, 41, 61, 89, 409, 449, 499, 881, 991, 6469, 6949, 9001, 9049, 9649, 9949, 60649, 666649, 946669, 60000049, 66000049, 66600049 (OEIS A071062)

### Newman–Shanks–Williams primes

Newman–Shanks–Williams numbers that are prime.

7, 41, 239, 9369319, 63018038201, 489133282872437279, 19175002942688032928599 (OEIS A088165)

### Non-generous primes

Primes *p* for which the least positive primitive root is not a primitive root of *p*2. Three such primes are known; it is not known whether there are more.

2, 40487, 6692367337 (OEIS A055578)

### Palindromic primes

Primes that remain the same when their decimal digits are read backwards.

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 (OEIS A002385)

### Palindromic wing primes

Primes of the form {\displaystyle {\frac {a{\big (}10^{m}-1{\big )}}{9}}\pm b\times 10^{\frac {m-1}{2}}} with {\displaystyle 0\leq a\pm b<10}. This means all digits except the middle digit are equal.

101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 11311, 11411, 33533, 77377, 77477, 77977, 1114111, 1117111, 3331333, 3337333, 7772777, 7774777, 7778777, 111181111, 111191111, 777767777, 77777677777, 99999199999 (OEIS A077798)

### Partition primes

Partition function values that are prime.

2, 3, 5, 7, 11, 101, 17977, 10619863, 6620830889, 80630964769, 228204732751, 1171432692373, 1398341745571, 10963707205259, 15285151248481, 10657331232548839, 790738119649411319, 18987964267331664557 (OEIS A049575)

### Pell primes

Primes in the Pell number sequence *P*0 = 0, *P**1* = 1,
*P**n* = 2*P**n*−1 + *P**n*−2.

2, 5, 29, 5741, 33461, 44560482149, 1746860020068409, 68480406462161287469, 13558774610046711780701, 4125636888562548868221559797461449 (OEIS A086383)

### Permutable primes

Any permutation of the decimal digits is a prime.

2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 199, 311, 337, 373, 733, 919, 991, 1111111111111111111, 11111111111111111111111 (OEIS A003459)

It seems likely that all further permutable primes are repunits, i.e. contain only the digit 1.

### Perrin primes

Primes in the Perrin number sequence *P*(0) = 3, *P*(1) = 0, *P*(2) = 2,
*P*(*n*) = *P*(*n*−2) + *P*(*n*−3).

2, 3, 5, 7, 17, 29, 277, 367, 853, 14197, 43721, 1442968193, 792606555396977, 187278659180417234321, 66241160488780141071579864797 (OEIS A074788)

### Pierpont primes

Of the form 2*u*3*v* + 1 for some integers *u*,*v* ≥ 0.

These are also class 1- primes.

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 (OEIS A005109)

### Pillai primes

Primes *p* for which there exist *n* > 0 such that *p* divides *n*! + 1 and *n* does not divide *p* − 1.

23, 29, 59, 61, 67, 71, 79, 83, 109, 137, 139, 149, 193, 227, 233, 239, 251, 257, 269, 271, 277, 293, 307, 311, 317, 359, 379, 383, 389, 397, 401, 419, 431, 449, 461, 463, 467, 479, 499 (OEIS A063980)

### Primes of the form *n*4 + 1

Of the form *n*4 + 1.

2, 17, 257, 1297, 65537, 160001, 331777, 614657, 1336337, 4477457, 5308417, 8503057, 9834497, 29986577, 40960001, 45212177, 59969537, 65610001, 126247697, 193877777, 303595777, 384160001, 406586897, 562448657, 655360001 (OEIS A037896)

### Primeval primes

Primes for which there are more prime permutations of some or all the decimal digits than for any smaller number.

2, 13, 37, 107, 113, 137, 1013, 1237, 1367, 10079 (OEIS A119535)

### Primorial primes

Of the form *p**n*# ± 1.

3, 5, 7, 29, 31, 211, 2309, 2311, 30029, 200560490131, 304250263527209, 23768741896345550770650537601358309 (union of OEIS A057705 and OEIS A018239)

### Proth primes

Of the form *k*×2*n* + 1, with odd *k* and *k* < 2*n*.

3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857 (OEIS A080076)

### Pythagorean primes

Of the form 4*n* + 1.

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 (OEIS A002144)

### Prime quadruplets

Lihat pula: § Cousin primes, § Twin primes, dan § Prime triplets
Where (*p*, *p*+2, *p*+6, *p*+8) are all prime.

(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) (OEIS A007530, OEIS A136720, OEIS A136721, OEIS A090258)

### Quartan primes

Of the form *x*4 + *y*4, where *x*,*y* > 0.

2, 17, 97, 257, 337, 641, 881 (OEIS A002645)

### Ramanujan primes

Integers *R**n* that are the smallest to give at least *n* primes from *x*/2 to *x* for all *x* ≥ *R**n* (all such integers are primes).

2, 11, 17, 29, 41, 47, 59, 67, 71, 97, 101, 107, 127, 149, 151, 167, 179, 181, 227, 229, 233, 239, 241, 263, 269, 281, 307, 311, 347, 349, 367, 373, 401, 409, 419, 431, 433, 439, 461, 487, 491 (OEIS A104272)

### Regular primes

Primes *p* that do not divide the class number of the *p*-th cyclotomic field.

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 (OEIS A007703)

### Repunit primes

Primes containing only the decimal digit 1.

11, 1111111111111111111 (19 digits), 11111111111111111111111 (23 digits) (OEIS A004022)

The next have 317, 1031, 49081, 86453, 109297, 270343 digits (OEIS A004023)

### Residue classes of primes

Of the form *an* + *d* for fixed integers *a* and *d*. Also called primes congruent to *d* modulo *a*.

The primes of the form 2*n*+1 are the odd primes, including all primes other than 2. Some sequences have alternate names: 4*n*+1 are Pythagorean primes, 4*n*+3 are the integer Gaussian primes, and 6*n*+5 are the Eisenstein primes (with 2 omitted). The classes 10*n*+*d* (*d* = 1, 3, 7, 9) are primes ending in the decimal digit *d*.

2*n*+1: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 (OEIS A065091)  

4*n*+1: 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137 (OEIS A002144)  

4*n*+3: 3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107 (OEIS A002145)  

6*n*+1: 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139 (OEIS A002476)  

6*n*+5: 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113 (OEIS A007528)  

8*n*+1: 17, 41, 73, 89, 97, 113, 137, 193, 233, 241, 257, 281, 313, 337, 353 (OEIS A007519)  

8*n*+3: 3, 11, 19, 43, 59, 67, 83, 107, 131, 139, 163, 179, 211, 227, 251 (OEIS A007520)  

8*n*+5: 5, 13, 29, 37, 53, 61, 101, 109, 149, 157, 173, 181, 197, 229, 269 (OEIS A007521)  

8*n*+7: 7, 23, 31, 47, 71, 79, 103, 127, 151, 167, 191, 199, 223, 239, 263 (OEIS A007522)  

10*n*+1: 11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 211, 241, 251, 271, 281 (OEIS A030430)  

10*n*+3: 3, 13, 23, 43, 53, 73, 83, 103, 113, 163, 173, 193, 223, 233, 263 (OEIS A030431)  

10*n*+7: 7, 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 197, 227, 257, 277 (OEIS A030432)  

10*n*+9: 19, 29, 59, 79, 89, 109, 139, 149, 179, 199, 229, 239, 269, 349, 359 (OEIS A030433)  

12*n*+1: 13, 37, 61, 73, 97, 109, 157, 181, 193, 229, 241, 277, 313, 337, 349 (OEIS A068228)  

12*n*+5: 5, 17, 29, 41, 53, 89, 101, 113, 137, 149, 173, 197, 233, 257, 269 (OEIS A040117)  

12*n*+7: 7, 19, 31, 43, 67, 79, 103, 127, 139, 151, 163, 199, 211, 223, 271 (OEIS A068229)  

12*n*+11: 11, 23, 47, 59, 71, 83, 107, 131, 167, 179, 191, 227, 239, 251, 263 (OEIS A068231)

### Safe primes

Where *p* and (*p*−1) / 2 are both prime.

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 (OEIS A005385)

### Self primes in base 10

Primes that cannot be generated by any integer added to the sum of its decimal digits.

3, 5, 7, 31, 53, 97, 211, 233, 277, 367, 389, 457, 479, 547, 569, 613, 659, 727, 839, 883, 929, 1021, 1087, 1109, 1223, 1289, 1447, 1559, 1627, 1693, 1783, 1873 (OEIS A006378)

### Sexy primes

Where (*p*, *p* + 6) are both prime.

(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) (OEIS A023201, OEIS A046117)

### Smarandache–Wellin primes

Primes that are the concatenation of the first *n* primes written in decimal.

2, 23, 2357 (OEIS A069151)

The fourth Smarandache-Wellin prime is the 355-digit concatenation of the first 128 primes that end with 719.

### Solinas primes

Of the form 2*a* ± 2*b* ± 1, where 0 < *b* < *a*.

3, 5, 7, 11, 13 (OEIS A165255)

### Sophie Germain primes

Where *p* and 2*p* + 1 are both prime.

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 (OEIS A005384)

### Stern primes

Primes that are not the sum of a smaller prime and twice the square of a nonzero integer.

2, 3, 17, 137, 227, 977, 1187, 1493 (OEIS A042978)

Hingga 2011[update], these are the only known Stern primes, and possibly the only existing.

### Strobogrammatic primes

Primes that are also a prime number when rotated upside down. (This, as with its alphabetic counterpart the ambigram, is dependent upon the typeface.)

Using 0, 1, 8 and 6/9:

11, 101, 181, 619, 16091, 18181, 19861, 61819, 116911, 119611, 160091, 169691, 191161, 196961, 686989, 688889 (barisan A007597 pada OEIS)

### Super-primes

Primes with a prime index in the sequence of prime numbers (the 2nd, 3rd, 5th, ... prime).

3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, 211, 241, 277, 283, 331, 353, 367, 401, 431, 461, 509, 547, 563, 587, 599, 617, 709, 739, 773, 797, 859, 877, 919, 967, 991 (OEIS A006450)

### Supersingular primes

There are exactly fifteen supersingular primes:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71 (OEIS A002267)

### Thabit primes

Of the form 3×2*n* − 1.

2, 5, 11, 23, 47, 191, 383, 6143, 786431, 51539607551, 824633720831, 26388279066623, 108086391056891903, 55340232221128654847, 226673591177742970257407 (OEIS A007505)

The primes of the form 3×2*n* + 1 are related.

7, 13, 97, 193, 769, 12289, 786433, 3221225473, 206158430209, 6597069766657 (OEIS A039687)

### Prime triplets

Lihat pula: § Cousin primes, § Twin primes, dan § Prime quadruplets
Where (*p*, *p*+2, *p*+6) or (*p*, *p*+4, *p*+6) are all prime.

(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) (OEIS A007529, OEIS A098414, OEIS A098415)

### Truncatable prime

#### Left-truncatable

Primes that remain prime when the leading decimal digit is successively removed.

2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 113, 137, 167, 173, 197, 223, 283, 313, 317, 337, 347, 353, 367, 373, 383, 397, 443, 467, 523, 547, 613, 617, 643, 647, 653, 673, 683 (OEIS A024785)

#### Right-truncatable

Primes that remain prime when the least significant decimal digit is successively removed.

2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797, 2333, 2339, 2393, 2399, 2939, 3119, 3137, 3733, 3739, 3793, 3797 (OEIS A024770)

#### Two-sided

Primes that are both left-truncatable and right-truncatable. There are exactly fifteen two-sided primes:

2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397 (OEIS A020994)

### Twin primes

Lihat pula: § Cousin primes, § Prime triplets, dan § Prime quadruplets
Where (*p*, *p*+2) are both prime.

(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) (OEIS A001359, OEIS A006512)

### Unique primes

The list of primes *p* for which the period length of the decimal expansion of 1/*p* is unique (no other prime gives the same period).

3, 11, 37, 101, 9091, 9901, 333667, 909091, 99990001, 999999000001, 9999999900000001, 909090909090909091, 1111111111111111111, 11111111111111111111111, 900900900900990990990991 (OEIS A040017)

### Wagstaff primes

Of the form (2*n* + 1) / 3.

3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, 201487636602438195784363, 845100400152152934331135470251, 56713727820156410577229101238628035243 (OEIS A000979)

Values of *n*:

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 (OEIS A000978)

### Wall–Sun–Sun primes

A prime *p* > 5, if *p*2 divides the Fibonacci number {\displaystyle F\_{p-\left({\frac {p}{5}}\right)}}, where the Legendre symbol {\displaystyle \left({\frac {p}{5}}\right)} is defined as

{\displaystyle \left({\frac {p}{5}}\right)={\begin{cases}1&{\textrm {if}}\;p\equiv \pm 1{\pmod {5}}\\-1&{\textrm {if}}\;p\equiv \pm 2{\pmod {5}}.\end{cases}}}
Hingga 2018[update], no Wall-Sun-Sun primes are known.

### Weakly prime numbers

Primes that having any one of their (base 10) digits changed to any other value will always result in a composite number.

294001, 505447, 584141, 604171, 971767, 1062599, 1282529, 1524181, 2017963, 2474431, 2690201, 3085553, 3326489, 4393139 (OEIS A050249)

### Wieferich primes

Primes *p* such that *a**p* − 1 ≡ 1 (mod *p*2) for fixed integer *a* > 1.

2*p* − 1 ≡ 1 (mod *p*2): 1093, 3511 (OEIS A001220)  

3*p* − 1 ≡ 1 (mod *p*2): 11, 1006003 (OEIS A014127)  

4*p* − 1 ≡ 1 (mod *p*2): 1093, 3511  

5*p* − 1 ≡ 1 (mod *p*2): 2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801 (OEIS A123692)  

6*p* − 1 ≡ 1 (mod *p*2): 66161, 534851, 3152573 (OEIS A212583)  

7*p* − 1 ≡ 1 (mod *p*2): 5, 491531 (OEIS A123693)  

8*p* − 1 ≡ 1 (mod *p*2): 3, 1093, 3511  

9*p* − 1 ≡ 1 (mod *p*2): 2, 11, 1006003  

10*p* − 1 ≡ 1 (mod *p*2): 3, 487, 56598313 (OEIS A045616)  

11*p* − 1 ≡ 1 (mod *p*2): 71  

12*p* − 1 ≡ 1 (mod *p*2): 2693, 123653 (OEIS A111027)  

13*p* − 1 ≡ 1 (mod *p*2): 2, 863, 1747591 (OEIS A128667)  

14*p* − 1 ≡ 1 (mod *p*2): 29, 353, 7596952219 (OEIS A234810)  

15*p* − 1 ≡ 1 (mod *p*2): 29131, 119327070011 (OEIS A242741)  

16*p* − 1 ≡ 1 (mod *p*2): 1093, 3511  

17*p* − 1 ≡ 1 (mod *p*2): 2, 3, 46021, 48947 (OEIS A128668)  

18*p* − 1 ≡ 1 (mod *p*2): 5, 7, 37, 331, 33923, 1284043 (OEIS A244260)  

19*p* − 1 ≡ 1 (mod *p*2): 3, 7, 13, 43, 137, 63061489 (OEIS A090968)  

20*p* − 1 ≡ 1 (mod *p*2): 281, 46457, 9377747, 122959073 (OEIS A242982)  

21*p* − 1 ≡ 1 (mod *p*2): 2  

22*p* − 1 ≡ 1 (mod *p*2): 13, 673, 1595813, 492366587, 9809862296159 (OEIS A298951)  

23*p* − 1 ≡ 1 (mod *p*2): 13, 2481757, 13703077, 15546404183, 2549536629329 (OEIS A128669)  

24*p* − 1 ≡ 1 (mod *p*2): 5, 25633  

25*p* − 1 ≡ 1 (mod *p*2): 2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801

Hingga 2018[update], these are all known Wieferich primes with *a* ≤ 25.

### Wilson primes

Primes *p* for which *p*2 divides (*p*−1)! + 1.

5, 13, 563 (OEIS A007540)

Hingga 2018[update], these are the only known Wilson primes.

### Wolstenholme primes

Primes *p* for which the binomial coefficient {\displaystyle {{2p-1} \choose {p-1}}\equiv 1{\pmod {p^{4}}}.}

16843, 2124679 (OEIS A088164)

Hingga 2018[update], these are the only known Wolstenholme primes.

### Woodall primes

Of the form *n*×2*n* − 1.

7, 23, 383, 32212254719, 2833419889721787128217599, 195845982777569926302400511, 4776913109852041418248056622882488319 (OEIS A050918)

Referensi
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1. ↑  Lehmer, D. N. (1982). *List of prime numbers from 1 to 10,006,721*. **165**. Washington D.C.: Carnegie Institution of Washington. OL 16553580M. OL16553580M.
2. ↑  Tomás Oliveira e Silva, Goldbach conjecture verification Diarsipkan 24 May 2011 di Wayback Machine.. Retrieved 16 July 2013
3. ↑  (barisan A080127 pada OEIS)
4. ↑  Jens Franke (29 Juli 2010). "Conditional Calculation of pi(1024)". Diarsipkan dari versi asli tanggal 24 Agustus 2014. Diakses tanggal 17 Mei 2011.  Parameter `|url-status=` yang tidak diketahui akan diabaikan (bantuan)
5. 1 2  OEIS A018239 termasuk includes 2 = darab kosong mengenai 0 prima pertama ditambah of 1, tetapi 2 dikecualikan dalam daftar ini.
6. ↑  Boklan, Kent D.; Conway, John H. (2016). "Expect at most one billionth of a new Fermat Prime!".  *arΧiv:1605.01371* [math.NT].
7. ↑  Boyd, D. W. (1994). "A *p*-adic Study of the Partial Sums of the Harmonic Series". *Experimental Mathematics*. **3** (4): 287–302. doi:10.1080/10586458.1994.10504298. Zbl 0838.11015. CiteSeerX: 10.1.1.56.7026. Diarsipkan dari versi asli tanggal 27 January 2016.  Parameter `|url-status=` yang tidak diketahui akan diabaikan (bantuan)
8. 1 2  Johnson, W. (1975). "Irregular Primes and Cyclotomic Invariants" (PDF). *Mathematics of Computation*. AMS. **29** (129): 113–120. doi:10.2307/2005468. JSTOR 2005468. Diarsipkan dari versi asli (PDF) tanggal 20 December 2010.  Parameter `|url-status=` yang tidak diketahui akan diabaikan (bantuan)
9. ↑  It varies whether *L*0 = 2 is included in the Lucas numbers.
10. ↑  Sloane, N.J.A. (ed.). "Sequence A121091 (Smallest nexus prime of the form n^p - (n-1)^p, where p is an odd prime)". *On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.
11. ↑  Sloane, N.J.A. (ed.). "Sequence A121616 (Primes of form (n+1)^5 - n^5)". *On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.
12. ↑  Sloane, N.J.A. (ed.). "Sequence A121618 (Nexus primes of order 7 or primes of form n^7 - (n-1)^7)". *On-Line Encyclopedia of Integer Sequences*. OEIS Foundation.
13. ↑  Paszkiewicz, Andrzej (2009). "A new prime {\displaystyle p} for which the least primitive root {\displaystyle ({\textrm {mod}}p)} and the least primitive root {\displaystyle ({\textrm {mod}}p^{2})} are not equal" (PDF). *Math. Comp*. American Mathematical Society. **78**: 1193–1195. Bibcode:2009MaCom..78.1193P. doi:10.1090/S0025-5718-08-02090-5.
14. ↑  Caldwell, C.; Dubner, H. (1996–97). "The near repdigit primes {\displaystyle A\_{n-k-1}B\_{1}A\_{k}}, especially {\displaystyle 9\_{n-k-1}8\_{1}9\_{k}}". *Journal of Recreational Mathematics*. **28** (1): 1–9.
15. ↑  Lal, M. (1967). "Primes of the Form n4 + 1" (PDF). *Mathematics of Computation*. AMS. **21**: 245–247. doi:10.1090/S0025-5718-1967-0222007-9. ISSN 1088-6842. Diarsipkan dari versi asli (PDF) tanggal 13 January 2015.  Parameter `|url-status=` yang tidak diketahui akan diabaikan (bantuan)
16. ↑  Bohman, J. (1973). "New primes of the form *n*4 + 1". *BIT Numerical Mathematics*. Springer. **13** (3): 370–372. doi:10.1007/BF01951947. ISSN 1572-9125.
17. ↑  Ribenboim, P. (22 February 1996). *The new book of prime number records*. New York: Springer-Verlag. hlm. 347. ISBN 0-387-94457-5.
18. ↑  "Mirimanoff's Congruence: Other Congruences". Diakses tanggal 26 January 2011.
19. ↑  Gallot, Y.; Moree, P.; Zudilin, W. (2011). "The Erdös-Moser equation 1*k* + 2*k* +...+ (m−1)*k* = m*k* revisited using continued fractions". *Mathematics of Computation*. American Mathematical Society. **80**: 1221–1237. arXiv:0907.1356 alt=Dapat diakses gratis. doi:10.1090/S0025-5718-2010-02439-1.
20. 1 2 3 4  Ribenboim, P. (2006). *Die Welt der Primzahlen* (PDF). Berlin: Springer. hlm. 240. ISBN 3-540-34283-4.  Parameter `|url-status=` yang tidak diketahui akan diabaikan (bantuan)