LIST OF PRIME NUMBERS

There are infinitely many prime numbers. The first 500 are listed below, followed by lists of the first prime numbers of various types in alphabetical order.

Contents

The first 500 prime numbers

Lists of primes by type

Primes with the same distance to the previous and next prime. 5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103

Of the form $(2^n\; -\; 1)^2\; -\; 2$. 7, 47, 223, 3967, 16127, 1046527, 16769023, 1073676287, 68718952447

Of the form $5(n^2-n)+1$. 11, 31, 61, 101, 151, 211, 281, 661, 911, 1051, 1201, 1361, 1901, 2311, 2531, 3001, 3251, 3511, 4651, 5281

Of the form (7''n''2 − 7''n'' + 2) / 2. 43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843

Of the form $n^2\; +\; (n\; +\; 1)^2$. 5, 13, 41, 61, 113, 181, 313, 421, 613, 761, 1013, 1201, 1301, 1741, 1861, 2113, 2381, 2521, 3121, 3613

Of the form (3''n''2 + 3''n'' + 2) / 2. 19, 31, 109, 199, 409, 571, 631, 829, 1489, 1999, 2341, 2971

(''p'', ''p'' + 4) are both prime. (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)

Of the form ''n'' · 2''n'' + 1. 3, 393050634124102232869567034555427371542904833

Of the form $2^\{2^p-1\}-1$, i.e. $2^\{(2^p-1)\}-1$, p prime. 7, 127, 2147483647, 170141183460469231731687303715884105727 As of August 2007, these are the only known double Mersenne primes (subset of Mersenne primes.)

Primes which become a different prime when their decimal digits are reversed. 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359

Of the form $2^\{2^n\}\; +\; 1$. 3, 5, 17, 257, 65537 As of August 2007, these are the only known Fermat primes.

17 The only prime Genocchi number is 17 (and -3 if ''negative primes'' are included).

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

Of the form $(2^n\; +\; 1)^2\; -\; 2$. 7, 23, 79, 1087, 66047, 263167, 16785407, 1073807359

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

Of the form ''x''''y'' + ''y''''x'' with 1 < ''x'' ≤ ''y''. 17, 593, 32993, 2097593

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

Of the form 2''n'' − 1. The first 12: 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727 As of August 2007, there are 44 known Mersenne primes. The 13th and 14th, respectively, have 157 and 183 digits.

Of the form $lfloor\; heta^\{3^\{n\}\};$ floor, where θ is Mills' constant. This form is prime for all positive integers ''n''. 2, 11, 1361, 2521008887, 16022236204009818131831320183

Primes that are the number of different ways of drawing non-intersecting chords on a circle between ''n'' points. 2, 127, 15511, 953467954114363

Newman-Shanks-Williams numbers that are prime. 7, 41, 239, 9369319, 63018038201, 489133282872437279, 19175002942688032928599

Of the form 2''n'' + 1. 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 "Odd primes" is a common term to exclude 2 which is the only even prime.

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

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

(''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)

(''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)

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

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

Integers ''Rn'' that are the smallest to give at least ''n'' primes from ''x''/2 to ''x'' for all ''x'' ≥ ''Rn'' (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

Primes containing only the decimal digit 1. 11, 1111111111111111111, 11111111111111111111111 The next have 317 and 1031 digits.

Primes that remain prime when the last decimal digit is successively removed. 2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239

''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

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

(''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)

Primes which are the concatenation of the first n primes written in decimal. 2, 23, 2357 The fourth Smarandache-Wellin prime is the concatenation of the first 128 primes which end with 719.

''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

Of the form 6''n''(''n'' - 1) + 1. 13, 37, 73, 181, 337, 433, 541, 661, 937, 1093, 2053, 2281, 2521, 3037, 3313

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 As of October 2006, these are the only known Stern primes, and possibly the only existing.

There are exactly fifteen supersingular primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71

Of the form 3 · 2''n'' - 1. 2, 5, 11, 23, 47, 191, 383, 6143

(''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), (521, 523), (569, 571), (599, 601), (617, 619), (641, 643), (659, 661)

Of the form (2''n'' + 1) / 3. 3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, 201487636602438195784363, 845100400152152934331135470251, 56713727820156410577229101238628035243 ''n'' values: 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

Wedderburn-Etherington numbers that are prime. 2, 3, 11, 23, 983, 2179, 24631, 3626149

Primes ''p'' for which ''p''2 divides 2''p'' − 1 − 1 1093, 3511 As of January 2007, these are the only known Wieferich primes.

Primes ''p'' for which ''p''2 divides (''p'' − 1)! + 1 5, 13, 563 As of January 2007, these are the only known Wilson primes.

Of the form ''n'' · 2''n'' − 1. 7, 23, 383, 32212254719, 2833419889721787128217599

External links

The first 500 prime numbers

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	163	167	173
179	181	191	193	197	199	211	223	227	229
233	239	241	251	257	263	269	271	277	281
283	293	307	311	313	317	331	337	347	349
353	359	367	373	379	383	389	397	401	409
419	421	431	433	439	443	449	457	461	463
467	479	487	491	499	503	509	521	523	541
547	557	563	569	571	577	587	593	599	601
607	613	617	619	631	641	643	647	653	659
661	673	677	683	691	701	709	719	727	733
739	743	751	757	761	769	773	787	797	809
811	821	823	827	829	839	853	857	859	863
877	881	883	887	907	911	919	929	937	941
947	953	967	971	977	983	991	997	1009	1013
1019	1021	1031	1033	1039	1049	1051	1061	1063	1069
1087	1091	1093	1097	1103	1109	1117	1123	1129	1151
1153	1163	1171	1181	1187	1193	1201	1213	1217	1223
1229	1231	1237	1249	1259	1277	1279	1283	1289	1291
1297	1301	1303	1307	1319	1321	1327	1361	1367	1373
1381	1399	1409	1423	1427	1429	1433	1439	1447	1451
1453	1459	1471	1481	1483	1487	1489	1493	1499	1511
1523	1531	1543	1549	1553	1559	1567	1571	1579	1583
1597	1601	1607	1609	1613	1619	1621	1627	1637	1657
1663	1667	1669	1693	1697	1699	1709	1721	1723	1733
1741	1747	1753	1759	1777	1783	1787	1789	1801	1811
1823	1831	1847	1861	1867	1871	1873	1877	1879	1889
1901	1907	1913	1931	1933	1949	1951	1973	1979	1987
1993	1997	1999	2003	2011	2017	2027	2029	2039	2053
2063	2069	2081	2083	2087	2089	2099	2111	2113	2129
2131	2137	2141	2143	2153	2161	2179	2203	2207	2213
2221	2237	2239	2243	2251	2267	2269	2273	2281	2287
2293	2297	2309	2311	2333	2339	2341	2347	2351	2357
2371	2377	2381	2383	2389	2393	2399	2411	2417	2423
2437	2441	2447	2459	2467	2473	2477	2503	2521	2531
2539	2543	2549	2551	2557	2579	2591	2593	2609	2617
2621	2633	2647	2657	2659	2663	2671	2677	2683	2687
2689	2693	2699	2707	2711	2713	2719	2729	2731	2741
2749	2753	2767	2777	2789	2791	2797	2801	2803	2819
2833	2837	2843	2851	2857	2861	2879	2887	2897	2903
2909	2917	2927	2939	2953	2957	2963	2969	2971	2999
3001	3011	3019	3023	3037	3041	3049	3061	3067	3079
3083	3089	3109	3119	3121	3137	3163	3167	3169	3181
3187	3191	3203	3209	3217	3221	3229	3251	3253	3257
3259	3271	3299	3301	3307	3313	3319	3323	3329	3331
3343	3347	3359	3361	3371	3373	3389	3391	3407	3413
3433	3449	3457	3461	3463	3467	3469	3491	3499	3511
3517	3527	3529	3533	3539	3541	3547	3557	3559	3571

Lists of primes by type

Below are listed the first prime numbers of many named forms and types. More details are in the article for the name. ''n'' is a natural number (including 0) in the definitions.
=== Balanced primes

Primes with the same distance to the previous and next prime.
5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103

Bell number primes ===
Primes that are the number of partitions of a set with ''n'' members.
2, 5, 877, 27644437, 35742549198872617291353508656626642567, 359334085968622831041960188598043661065388726959079837
=== Carol primes

Of the form $(2^n\; -\; 1)^2\; -\; 2$.
7, 47, 223, 3967, 16127, 1046527, 16769023, 1073676287, 68718952447

Centered decagonal primes

Of the form $5(n^2-n)+1$.
11, 31, 61, 101, 151, 211, 281, 661, 911, 1051, 1201, 1361, 1901, 2311, 2531, 3001, 3251, 3511, 4651, 5281

Centered heptagonal primes

Of the form (7''n''² − 7''n'' + 2) / 2.
43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843

Centered square primes

Of the form $n^2\; +\; (n\; +\; 1)^2$.
5, 13, 41, 61, 113, 181, 313, 421, 613, 761, 1013, 1201, 1301, 1741, 1861, 2113, 2381, 2521, 3121, 3613

Centered triangular primes

Of the form (3''n''² + 3''n'' + 2) / 2.
19, 31, 109, 199, 409, 571, 631, 829, 1489, 1999, 2341, 2971

Chen primes ===
''p'' is prime and ''p'' + 2 is either a prime or semiprime.
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
=== Cousin primes

(''p'', ''p'' + 4) are both prime.
(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)

Cuban primes ===
Of the form $frac\{x^3-y^3\}\{x-y\}$, $x=y+1$:
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
Of the form $frac\{x^3-y^3\}\{x-y\}$, $x=y+2$:
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
=== Cullen primes

Of the form ''n'' · 2^''n'' + 1.
3, 393050634124102232869567034555427371542904833

Dihedral primes ===
Primes that remain prime when read upside down or mirrored in a seven-segment display.
2, 11, 101, 181, 1181, 1811, 18181, 108881, 110881, 118081, 120121, 121021, 121151, 150151, 151051, 151121, 180181, 180811, 181081
=== Double Mersenne primes

Of the form $2^\{2^p-1\}-1$, i.e. $2^\{(2^p-1)\}-1$, p prime.
7, 127, 2147483647, 170141183460469231731687303715884105727
As of August 2007, these are the only known double Mersenne primes (subset of Mersenne primes.)

Eisenstein primes without imaginary part ===
Eisenstein integers that are irreducible and real numbers.
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
=== Emirps

Primes which become a different prime when their decimal digits are reversed.
13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359

Euclid primes ===
Of the form ''p''_''n''# + 1.
3, 7, 31, 211, 2311
=== Even prime ===
Of the form 2''n''.
2
The only even prime is 2. 'Humorously', 2 is therefore frequently called "the oddest prime". [1]
=== Factorial primes ===
Of the form ''n''! − 1 or ''n''! + 1.
2, 3, 5, 7, 23, 719, 5039, 39916801, 479001599, 87178291199
=== Fermat primes

Of the form $2^\{2^n\}\; +\; 1$.
3, 5, 17, 257, 65537
As of August 2007, these are the only known Fermat primes.

Fibonacci primes ===
Primes in the Fibonacci sequence ''F''₀ = 0, ''F''_''1'' = 1,
''F''_''n'' = ''F''_''n''-1 + ''F''_''n''-2.
2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073
=== Gaussian primes ===
Prime elements of the Gaussian integers.
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
=== Genocchi number primes

17
The only prime Genocchi number is 17 (and -3 if ''negative primes'' are included).

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
=== 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

Highly cototient number primes ===
Primes that are a cototient more often than any integer below it except 1.
23, 47, 59, 83, 89, 113, 167, 269, 389, 419, 509, 659, 839
=== Irregular primes ===
Odd primes ''p'' which 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
=== Kynea primes

Of the form $(2^n\; +\; 1)^2\; -\; 2$.
7, 23, 79, 1087, 66047, 263167, 16785407, 1073807359

Left-truncatable primes

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

Leyland primes

Of the form ''x''^''y'' + ''y''^''x'' with 1 < ''x'' ≤ ''y''.
17, 593, 32993, 2097593

Long primes ===
Primes ''p'' for which, in a given base ''b'', gives a cyclic number. 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
=== 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
=== 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

Markov primes ===
Primes ''p'' for which there exist integers x and y such that $x^2\; +\; y^2\; +\; p^2\; =\; 3xyp$.
2, 5, 13, 29, 89, 233, 433, 1597, 2897
=== Mersenne primes

Of the form 2^''n'' − 1. The first 12:
3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727
As of August 2007, there are 44 known Mersenne primes. The 13th and 14th, respectively, have 157 and 183 digits.

Mills primes

Of the form $lfloor\; heta^\{3^\{n\}\};$
floor, where θ is Mills' constant. This form is prime for all positive integers ''n''.
2, 11, 1361, 2521008887, 16022236204009818131831320183

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
=== Motzkin primes

Primes that are the number of different ways of drawing non-intersecting chords on a circle between ''n'' points.
2, 127, 15511, 953467954114363

Newman-Shanks-Williams primes

Newman-Shanks-Williams numbers that are prime.
7, 41, 239, 9369319, 63018038201, 489133282872437279, 19175002942688032928599

Odd primes

Of the form 2''n'' + 1.
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
"Odd primes" is a common term to exclude 2 which is the only even prime.

Padovan primes ===
Primes in the Padovan sequence $P(0)=P(1)=P(2)=1$, $P(n)=P(n-2)+P(n-3)$.
2, 3, 5, 7, 37, 151, 3329, 23833
=== 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

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
=== 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
It seems likely that all other 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
=== Pierpont primes ===
Of the form $2^u\; 3^v\; +\; 1$ for some integers ''u'',''v'' ≥ 0.
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
=== 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

Prime quadruplets

(''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)

Prime triplets

(''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)

Primorial primes ===
Of the form ''p_n''# − 1 or ''p_n''# + 1.
5, 7, 29, 31, 211, 2309, 2311, 30029
=== 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

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

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

Regular primes ===
Primes ''p'' which 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
=== Repunit primes

Primes containing only the decimal digit 1.
11, 1111111111111111111, 11111111111111111111111
The next have 317 and 1031 digits.

Right-truncatable primes

Primes that remain prime when the last decimal digit is successively removed.
2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239

Safe primes

''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

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

Sexy primes

(''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)

Smarandache-Wellin primes

Primes which are the concatenation of the first n primes written in decimal.
2, 23, 2357
The fourth Smarandache-Wellin prime is the concatenation of the first 128 primes which end with 719.

Sophie Germain primes

''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

Star primes

Of the form 6''n''(''n'' - 1) + 1.
13, 37, 73, 181, 337, 433, 541, 661, 937, 1093, 2053, 2281, 2521, 3037, 3313

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
As of October 2006, these are the only known Stern primes, and possibly the only existing.

Supersingular primes

There are exactly fifteen supersingular primes:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71

Thabit number primes

Of the form 3 · 2^''n'' - 1.
2, 5, 11, 23, 47, 191, 383, 6143

Twin primes

(''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), (521, 523), (569, 571), (599, 601), (617, 619), (641, 643), (659, 661)

Unique primes ===
Primes ''p'' for which the period length of 1/''p'' is unique (no other prime gives the same).
3, 11, 37, 101, 9091, 9901, 333667
=== Wagstaff primes

Of the form (2^''n'' + 1) / 3.
3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, 201487636602438195784363, 845100400152152934331135470251, 56713727820156410577229101238628035243
''n'' values:
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

Wedderburn-Etherington number primes

Wedderburn-Etherington numbers that are prime.
2, 3, 11, 23, 983, 2179, 24631, 3626149

Wieferich primes

Primes ''p'' for which ''p''² divides 2^{''p'' − 1} − 1
1093, 3511
As of January 2007, these are the only known Wieferich primes.

Wilson primes

Primes ''p'' for which ''p''² divides (''p'' − 1)! + 1
5, 13, 563
As of January 2007, these are the only known Wilson primes.

Wolstenholme primes ===
Primes ''p'' for which the binomial coefficient $\{\{2p-1\}choose\{p-1\}\}\; equiv\; 1\; pmod\{p^4\}$.
16843, 2124679
As of August 2007, these are the only known Wolstenholme primes.
=== Woodall primes =

Of the form ''n'' · 2^''n'' − 1.
7, 23, 383, 32212254719, 2833419889721787128217599

See also ==

★ Gigantic prime ★ Illegal prime ★ Largest known prime ★ List of numbers ★ Prime ideal ★ Prime model

★ Probable prime ★ Strobogrammatic prime ★ Strong prime ★ Titanic prime ★ Wall-Sun-Sun prime ★ Weak prime ★ Wieferich pair

External links

★ Lists of Primes at the Prime Pages.

★ Interface to a list of the first 98 million primes (primes less than 8,000,000,000)

★ The first 130 million primes