List of prime numbers - Definition and Overview

This page contains a list of the first 500 prime numbers and lists of prime numbers by specific categorizations.

The first 500 prime numbers

List of unique primes

3, 11, 37, 101, 9091, 9901, 333667

List of twin primes

(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)

List of prime quadruplets

(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, 18429), (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, 97483, 97487, 97489), (99131, 99133, 99137, 99139)

List of Mersenne primes

As of mid 2004, there are only 41 known Mersenne primes. Listed below are the first ten, they get very large very quickly.

3, 7, 31, 127, 8191, 131071, 524827, 2147483647, 2305843009213693951

List of Fermat primes

As of mid 2004, these are the only known Fermat primes.

3, 5, 17, 257, 65537

List of Sophie Germain primes

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

List of Wilson primes

As of 2003, these are the only known Wilson primes.

5, 13, 563

List of Wolstenholme primes

As of 2003, these are the only known Wolstenholme primes.

16843, 2124679

List of factorial primes

2, 3, 5, 7, 23, 719, 5039, 39916801, 479001599, 87178291199

List of primorial primes

5, 7, 29, 31, 211, 2309, 2311, 30029

List of palindromic primes

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

List of cuban primes

Cuban primes of the form (x³ - y³) / (x - y), x is 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

Cuban primes of the form (x³ - y³) / (x - y), x is 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

List of Smarandache-Wellin primes

2, 23, 2357

List of lucky primes

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

See also

• List of numbers

External links

• Lists of Primes (http://www.utm.edu/research/primes/lists/) at the Prime Pages.
• Interface to a list of the first 98 million primes (http://www.rsok.com/~jrm/printprimes.html) (primes less than 2,000,000,000)