Prime Numbers

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

How To Use It

You can check single numbers, such as 661097, 1022387, or 2.

You can also compare various numbers with each other. For example:

• 31 and 43787: have the same number of properties.
• 43 and 1022387: have the same number of properties.
• 3 and 7: 7 belongs to much more prime types than 3.

You can also learn, that:

• 100th twin prime is {3821, 3823}
• 5th fermat prime is {3821, 65537}
• First 100 lucky primes have values between 3 and 3307.

Most Popular

The most popular pages are:

• First 100 prime numbers
• First 1000 prime numbers
• Prime numbers up to 1000
• Visualization of number of types into which prime numbers belong
• Visualization of density of different prime number types

Numbers belonging to highest number of classes are: 7: 37, 5: 36, 11: 36, 17: 36, 13: 32, 23: 30, 3: 29, 2: 26, 47: 21, 97: 20, 113: 20, 107: 19, 109: 19, 19: 18, 31: 18, 37: 18, 41: 18, 53: 18, 101: 18, 193: 18, 1487: 18, 19421: 18, 67: 17, 73: 17, 1873: 17, 19427: 17, 43781: 17, 43787: 17, 191: 16, 257: 16, 5653: 16, 12113: 16, 16063: 16, 21017: 16, 43789: 16, 195737: 16, 661097: 16, 313: 15, 647: 15, 15733: 15, 16061: 15, 19423: 15, 32057: 15, 43783: 15, 55337: 15, 88813: 15, 101113: 15, 144167: 15, 165707: 15, 166847: 15

Additive prime, Bell prime, Carol prime, Centered decagonal prime, Centered heptagonal prime, Centered square prime, Centered triangular prime, Chen prime, Class 1+ prime, Cousin prime, Cuban prime 1, Cuban prime 2, Cullen prime, Dihedral prime, Double mersenne prime, Emirps, Euclid prime, Factorial prime, Fermat prime, Fibonacci prime, Genocchi prime, Good prime, Happy prime, Harmonic prime, Isolated prime, Kynea prime, Left-truncatable prime, Leyland prime, Long prime, Lucas prime, Lucky prime, Mersenne prime, Mills prime, Multiplicative prime, Palindromic prime, Pierpont prime, Pierpont prime of the 2nd kind, Prime, Prime quadruplet, Prime quintuplet 1, Prime quintuplet 2, Prime sextuplet, Prime triplet, Proth prime, Pythagorean prime, Quartan prime, Restricted left-truncatable prime, Restricted right-truncatable prime, Right-truncatable prime, Safe prime, Semiprime, Sexy prime, Sexy prime quadruplets, Sexy prime triplet, Solinas prime, Sophie germain prime, Super prime, Thabit prime, Thabit prime of the 2nd kind, Twin prime, Two-sided prime, Ulam prime, Wagstaff prime, Weakly prime, Wedderburn-etherington prime, Wilson prime, Woodall prime

Primes such that the sum of digits is a prime. Learn more about Additive primes

First 20: 2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 113, 131, 137, 139, 151

Checkout list of first: 10, 50, 100, 500, 1000 additive primes. You can also check all additive primes.

Checkout additive primes up to: 100, 500, 1000, 10000.

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Primes that are the number of partitions of a set with n members. Learn more about Bell primes

First 3: 2, 5, 877

Checkout list of first: 10 bell primes. You can also check all bell primes.

Checkout bell primes up to: 100, 500, 1000.

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Primes of the form ((2^n)−1)^2 − 2. Learn more about Carol primes

First 6: 7, 47, 223, 3967, 16127, 1046527

Checkout list of first: 10 carol primes. You can also check all carol primes.

Checkout carol primes up to: 100, 500, 1000, 10000.

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Primes of the form 5(n^2 + n) + 1. Learn more about Centered decagonal primes

First 20: 11, 31, 61, 101, 151, 211, 281, 661, 911, 1051, 1201, 1361, 1531, 1901, 2311, 2531, 3001, 3251, 3511, 4651

Checkout list of first: 10, 50, 100, 500 centered decagonal primes. You can also check all centered decagonal primes.

Checkout centered decagonal primes up to: 100, 500, 1000, 10000.

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Primes of the form (7n^2 − 7n + 2) / 2. Learn more about Centered heptagonal primes

First 20: 43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843, 3697, 4663, 5741, 8233, 9283, 10781, 11173, 12391, 14561, 18397

Checkout list of first: 10, 50, 100, 500 centered heptagonal primes. You can also check all centered heptagonal primes.

Checkout centered heptagonal primes up to: 100, 500, 1000, 10000.

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Primes of the form n^2 + (n+1)^2. Learn more about Centered square primes

First 20: 5, 13, 41, 61, 113, 181, 313, 421, 613, 761, 1013, 1201, 1301, 1741, 1861, 2113, 2381, 2521, 3121, 3613

Checkout list of first: 10, 50, 100, 500 centered square primes. You can also check all centered square primes.

Checkout centered square primes up to: 100, 500, 1000, 10000.

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Primes of the form (3n^2 + 3n + 2) / 2. Learn more about Centered triangular primes

First 20: 19, 31, 109, 199, 409, 571, 631, 829, 1489, 1999, 2341, 2971, 3529, 4621, 4789, 7039, 7669, 8779, 9721, 10459

Checkout list of first: 10, 50, 100, 500 centered triangular primes. You can also check all centered triangular primes.

Checkout centered triangular primes up to: 100, 500, 1000, 10000.

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A prime number p is called a Chen prime if p + 2 is either a prime or semiprime. Learn more about Chen primes

First 20: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89

Checkout list of first: 10, 50, 100, 500, 1000 chen primes. You can also check all chen primes.

Checkout chen primes up to: 100, 500, 1000, 10000.

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Primes of the form 2^u * 3^v - 1 for some integers u,v ≥ 0. Learn more about Class 1+ primes

First 20: 2, 3, 5, 7, 11, 17, 23, 31, 47, 53, 71, 107, 127, 191, 383, 431, 647, 863, 971, 1151

Checkout list of first: 10, 50 class 1+ primes. You can also check all class 1+ primes.

Checkout class 1+ primes up to: 100, 500, 1000, 10000.

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If {p, p + 4} are primes then it becomes a prime cousin. Learn more about Cousin primes

First 20: {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}

Checkout list of first: 10, 50, 100, 500, 1000 cousin primes. You can also check all cousin primes.

Checkout cousin primes up to: 100, 500, 1000, 10000.

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Primes of the form 3y^2+3y+1. Learn more about Cuban primes 1

First 20: 7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919, 1657, 1801, 1951, 2269, 2437, 2791, 3169, 3571, 4219

Checkout list of first: 10, 50, 100, 500 Cuban primes 1. You can also check all Cuban primes 1.

Checkout Cuban primes 1 up to: 100, 500, 1000, 10000.

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Primes of the form 3y^2+6y+4. Learn more about Cuban primes 2

First 20: 13, 109, 193, 433, 769, 1201, 1453, 2029, 3469, 3889, 4801, 10093, 12289, 13873, 18253, 20173, 21169, 22189, 28813, 37633

Checkout list of first: 10, 50, 100 Cuban primes 2. You can also check all Cuban primes 2.

Checkout Cuban primes 2 up to: 100, 500, 1000, 10000.

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Primes of the form n×2^n + 1. Learn more about Cullen primes

First 1: 3

Checkout list of first: 10 cullen primes. You can also check all cullen primes.

Checkout cullen primes up to: 100.

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Primes that remain prime when read upside down or mirrored in a seven-segment display. Learn more about Dihedral primes

First 20: 2, 5, 11, 101, 181, 1181, 1811, 18181, 108881, 110881, 118081, 120121, 121021, 121151, 150151, 151051, 151121, 180181, 180811, 181081

Checkout list of first: 10, 50 dihedral primes. You can also check all dihedral primes.

Checkout dihedral primes up to: 100, 500, 1000, 10000.

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A subset of Mersenne primes of the form 2^(2^p −1) − 1 for prime p. Learn more about Double Mersenne primes

First 2: 7, 127

Checkout list of first: 10 double mersenne primes. You can also check all double mersenne primes.

Checkout double mersenne primes up to: 100, 500.

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An emirp is a prime number that results in a different prime when its decimal digits are reversed. Learn more about Emirps

First 20: 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389

Checkout list of first: 10, 50, 100, 500, 1000 Emirps. You can also check all Emirps.

Checkout Emirps up to: 100, 500, 1000, 10000.

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Primes of the form pn# + 1, where pn# is the nth primorial Learn more about Euclid primes

First 6: 2, 3, 7, 31, 211, 2311

Checkout list of first: 10 euclid primes. You can also check all euclid primes.

Checkout euclid primes up to: 100, 500, 1000, 10000.

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Primes of the form n! − 1 or n! + 1. Learn more about Factorial primes

First 7: 2, 3, 5, 7, 23, 719, 5039

Checkout list of first: 10 factorial primes. You can also check all factorial primes.

Checkout factorial primes up to: 100, 500, 1000, 10000.

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Primes of the form 2^(2^n) + 1. Learn more about Fermat primes

First 5: 3, 5, 17, 257, 65537

Checkout list of first: 10 fermat primes. You can also check all fermat primes.

Checkout fermat primes up to: 100, 500, 1000, 10000.

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Primes in the Fibonacci sequence. Learn more about Fibonacci primes

First 9: 2, 3, 5, 13, 89, 233, 1597, 28657, 514229

Checkout list of first: 10 fibonacci primes. You can also check all fibonacci primes.

Checkout fibonacci primes up to: 100, 500, 1000, 10000.

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Primes that are part of expansion of 2*n/(exp(n)+1) Learn more about Genocchi primes

First 1: 17

Checkout list of first: 10 genocchi primes. You can also check all genocchi primes.

Checkout genocchi primes up to: 100.

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Primes such that its square is greater than the product of any two primes at the same number of positions before and after it in the sequence of primes. Learn more about Good primes

First 20: 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149, 179, 191, 223, 227, 251, 257

Checkout list of first: 10, 50, 100, 500, 1000 good primes. You can also check all good primes.

Checkout good primes up to: 100, 500, 1000, 10000.

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Primes that eventually reach 1 under iteration of: x -> sum of squares of digits of x. Learn more about Happy primes

First 20: 7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379, 383

Checkout list of first: 10, 50, 100, 500, 1000 happy primes. You can also check all happy primes.

Checkout happy primes up to: 100, 500, 1000, 10000.

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Harmonic primes are harmoic. Learn more about Harmonic primes

First 20: 5, 13, 17, 23, 41, 67, 73, 79, 107, 113, 139, 149, 157, 179, 191, 193, 223, 239, 241, 251

Checkout list of first: 10, 50, 100, 500, 1000 harmonic primes. You can also check all harmonic primes.

Checkout harmonic primes up to: 100, 500, 1000, 10000.

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Primes p such that neither p−2 nor p+2 is prime. Learn more about Isolated primes

First 20: 2, 23, 37, 47, 53, 67, 79, 83, 89, 97, 113, 127, 131, 157, 163, 167, 173, 211, 223, 233

Checkout list of first: 10, 50, 100, 500, 1000 isolated primes. You can also check all isolated primes.

Checkout isolated primes up to: 100, 500, 1000, 10000.

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Primes of the form ((2^n)+1)^2 − 2. Learn more about Kynea primes

First 7: 2, 7, 23, 79, 1087, 66047, 263167

Checkout list of first: 10 kynea primes. You can also check all kynea primes.

Checkout kynea primes up to: 100, 500, 1000, 10000.

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Left-truncatable prime is a prime number which, contains no 0, and if the leading leftmost digit is successively removed, then all resulting numbers are prime. Learn more about Left-truncatable primes

First 20: 2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 113, 137, 167, 173, 197

Checkout list of first: 10, 50, 100, 500, 1000 left-truncatable primes. You can also check all left-truncatable primes.

Checkout left-truncatable primes up to: 100, 500, 1000, 10000.

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Primes of the form x^y + y^x with x and y are integers greater than 1. Learn more about Leyland primes

First 4: 3, 17, 593, 32993

Checkout list of first: 10 leyland primes. You can also check all leyland primes.

Checkout leyland primes up to: 100, 500, 1000, 10000.

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Long prime in base b is a prime number p such that the formula (b^(p-1)-1)/p (where p does not divide b) gives a cyclic number. Learn more about Long primes

First 20: 7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, 149, 167, 179, 181, 193, 223, 229, 233

Checkout list of first: 10, 50, 100, 500, 1000 long primes. You can also check all long primes.

Checkout long primes up to: 100, 500, 1000, 10000.

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Primes in the Lucas sequence. Learn more about Lucas primes

First 11: 2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349

Checkout list of first: 10, 50 lucas primes. You can also check all lucas primes.

Checkout lucas primes up to: 100, 500, 1000, 10000.

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Lucky primes is a natural number in a set which is generated by a certain sieve and are primes Learn more about Lucky primes

First 20: 3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193, 211, 223, 241, 283, 307, 331, 349

Checkout list of first: 10, 50, 100, 500, 1000 lucky primes. You can also check all lucky primes.

Checkout lucky primes up to: 100, 500, 1000, 10000.

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Primes of the form 2^n - 1. Learn more about Mersenne primes

First 7: 3, 7, 31, 127, 8191, 131071, 524287

Checkout list of first: 10 mersenne primes. You can also check all mersenne primes.

Checkout mersenne primes up to: 100, 500, 1000, 10000.

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Primes of the form floor(A^(3^n)) Learn more about Mills primes

First 3: 2, 11, 1361

Checkout list of first: 10 mills primes. You can also check all mills primes.

Checkout mills primes up to: 100, 500, 1000, 10000.

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Primes such that the product of digits is a prime. Learn more about Multiplicative primes

First 20: 2, 3, 5, 7, 13, 17, 31, 71, 113, 131, 151, 211, 311, 1117, 1151, 1171, 1511, 2111, 11113, 11117

Checkout list of first: 10, 50 multiplicative primes. You can also check all multiplicative primes.

Checkout multiplicative primes up to: 100, 500, 1000, 10000.

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A palindromic prime is a prime number that is also a palindromic number. Learn more about Palindromic primes

First 20: 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929

Checkout list of first: 10, 50, 100, 500 palindromic primes. You can also check all palindromic primes.

Checkout palindromic primes up to: 100, 500, 1000, 10000.

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Primes of the form 2^u * 3^v + 1. Learn more about Pierpont primes

First 20: 2, 3, 5, 7, 13, 17, 19, 37, 73, 97, 109, 163, 193, 257, 433, 487, 577, 769, 1153, 1297

Checkout list of first: 10, 50 pierpont primes. You can also check all pierpont primes.

Checkout pierpont primes up to: 100, 500, 1000, 10000.

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Primes of the form 2^u * 3^v - 1. Learn more about Pierpont primes of the 2nd kind

First 20: 2, 3, 5, 7, 11, 17, 23, 31, 47, 53, 71, 107, 127, 191, 383, 431, 647, 863, 971, 1151

Checkout list of first: 10, 50 Pierpont primes of the 2nd kind. You can also check all Pierpont primes of the 2nd kind.

Checkout Pierpont primes of the 2nd kind up to: 100, 500, 1000, 10000.

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A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Learn more about Prime numbers

First 20: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71

Checkout list of first: 10, 50, 100, 500, 1000 primes. You can also check all primes.

Checkout primes up to: 100, 500, 1000, 10000.

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If {p, p+2, p+6, p+8} are primes then it becomes a prime quadruplet. Learn more about Prime quadruplets

First 20: {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}

Checkout list of first: 10, 50, 100, 500 prime quadruplets. You can also check all prime quadruplets.

Checkout prime quadruplets up to: 100, 500, 1000, 10000.

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If {p-4, p, p+2, p+6, p+8} are primes then it becomes a prime quintuplet. Learn more about Prime quintuplets 1

First 20: {7, 11, 13, 17, 19}, {97, 101, 103, 107, 109}, {1867, 1871, 1873, 1877, 1879}, {3457, 3461, 3463, 3467, 3469}, {5647, 5651, 5653, 5657, 5659}, {15727, 15731, 15733, 15737, 15739}, {16057, 16061, 16063, 16067, 16069}, {19417, 19421, 19423, 19427, 19429}, {43777, 43781, 43783, 43787, 43789}, {79687, 79691, 79693, 79697, 79699}, {88807, 88811, 88813, 88817, 88819}, {101107, 101111, 101113, 101117, 101119}, {257857, 257861, 257863, 257867, 257869}, {266677, 266681, 266683, 266687, 266689}, {276037, 276041, 276043, 276047, 276049}, {284737, 284741, 284743, 284747, 284749}, {340927, 340931, 340933, 340937, 340939}, {354247, 354251, 354253, 354257, 354259}, {375247, 375251, 375253, 375257, 375259}, {402757, 402761, 402763, 402767, 402769}

Checkout list of first: 10, 50 prime quintuplet 1s. You can also check all prime quintuplet 1s.

Checkout prime quintuplet 1s up to: 100, 500, 1000, 10000.

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If {p, p+2, p+6, p+8, p+12} are primes then it becomes a prime quintuplet. Learn more about Prime quintuplets 2

First 20: {5, 7, 11, 13, 17}, {11, 13, 17, 19, 23}, {101, 103, 107, 109, 113}, {1481, 1483, 1487, 1489, 1493}, {16061, 16063, 16067, 16069, 16073}, {19421, 19423, 19427, 19429, 19433}, {21011, 21013, 21017, 21019, 21023}, {22271, 22273, 22277, 22279, 22283}, {43781, 43783, 43787, 43789, 43793}, {55331, 55333, 55337, 55339, 55343}, {144161, 144163, 144167, 144169, 144173}, {165701, 165703, 165707, 165709, 165713}, {166841, 166843, 166847, 166849, 166853}, {195731, 195733, 195737, 195739, 195743}, {201821, 201823, 201827, 201829, 201833}, {225341, 225343, 225347, 225349, 225353}, {247601, 247603, 247607, 247609, 247613}, {268811, 268813, 268817, 268819, 268823}, {326141, 326143, 326147, 326149, 326153}, {347981, 347983, 347987, 347989, 347993}

Checkout list of first: 10, 50 prime quintuplet 2s. You can also check all prime quintuplet 2s.

Checkout prime quintuplet 2s up to: 100, 500, 1000, 10000.

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If {p, p+4, p+6, p+10, p+12, p+16} are primes then it becomes a prime sextuplet. Learn more about Prime sextuplets

First 5: {7, 11, 13, 17, 19, 23}, {97, 101, 103, 107, 109, 113}, {16057, 16061, 16063, 16067, 16069, 16073}, {19417, 19421, 19423, 19427, 19429, 19433}, {43777, 43781, 43783, 43787, 43789, 43793}

Checkout list of first: 10 prime sextuplets. You can also check all prime sextuplets.

Checkout prime sextuplets up to: 100, 500, 1000, 10000.

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If {p, p + 2, p + 6} or {p, p + 4, p + 6} are primes then it becomes a prime triplet. Learn more about Prime triplets

First 20: {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}

Checkout list of first: 10, 50, 100, 500, 1000 prime triplets. You can also check all prime triplets.

Checkout prime triplets up to: 100, 500, 1000, 10000.

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Primes of the form k * 2^n + 1 where k is odd positive integer and n is a positive integer such that 2^n>k Learn more about Proth primes

First 20: 3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409

Checkout list of first: 10, 50, 100, 500 proth primes. You can also check all proth primes.

Checkout proth primes up to: 100, 500, 1000, 10000.

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Primes of the form 4n + 1 Learn more about Pythagorean primes

First 20: 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193

Checkout list of first: 10, 50, 100, 500, 1000 pythagorean primes. You can also check all pythagorean primes.

Checkout pythagorean primes up to: 100, 500, 1000, 10000.

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Primes of the form x^4 + y^4, where x > 0, y > 0 (and x and y are integers). Learn more about Quartan primes

First 20: 2, 17, 97, 257, 337, 641, 881, 1297, 2417, 2657, 3697, 4177, 4721, 6577, 10657, 12401, 14657, 14897, 15937, 16561

Checkout list of first: 10, 50, 100 quartan primes. You can also check all quartan primes.

Checkout quartan primes up to: 100, 500, 1000, 10000.

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Restricted left-truncatable prime is a prime which is left-truncatable and all of its left extensions are composite. Learn more about Restricted Left-truncatable primes

First 20: 2, 5, 773, 3373, 3947, 4643, 5113, 6397, 6967, 7937, 15647, 16823, 24373, 33547, 34337, 37643, 56983, 57853, 59743, 62383

Checkout list of first: 10, 50 restricted left-truncatable primes. You can also check all restricted left-truncatable primes.

Checkout restricted left-truncatable primes up to: 100, 500, 1000, 10000.

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Restricted right-truncatable prime is a prime which is right-truncatable and all of its right extensions are composite. Learn more about Restricted Right-truncatable primes

First 19: 53, 317, 599, 797, 2393, 3793, 3797, 7331, 23333, 23339, 31193, 31379, 37397, 73331, 373393, 593993, 719333, 739397, 739399

Checkout list of first: 10, 50 restricted right-truncatable primes. You can also check all restricted right-truncatable primes.

Checkout restricted right-truncatable primes up to: 100, 500, 1000, 10000.

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A right-truncatable prime is a prime which remains prime when the last rightmost digit is successively removed. Learn more about Right-truncatable primes

First 20: 2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373

Checkout list of first: 10, 50, 100 right-truncatable primes. You can also check all right-truncatable primes.

Checkout right-truncatable primes up to: 100, 500, 1000, 10000.

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A safe prime is a prime number of the form 2p + 1, where p is also a prime. Learn more about Safe primes

First 20: 5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587

Checkout list of first: 10, 50, 100, 500, 1000 safe primes. You can also check all safe primes.

Checkout safe primes up to: 100, 500, 1000, 10000.

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Semiprime is a natural number that is the product of two prime numbers. Learn more about Semiprimes

First 20: 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57

Checkout list of first: 10, 50, 100, 500, 1000 semiprimes. You can also check all semiprimes.

Checkout semiprimes up to: 100, 500, 1000, 10000.

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If {p, p + 6} are primes then they become sexy primes. Learn more about Sexy primes

First 20: {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}

Checkout list of first: 10, 50, 100, 500, 1000 sexy primes. You can also check all sexy primes.

Checkout sexy primes up to: 100, 500, 1000, 10000.

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If {p, p + 6, p + 12, p + 18} are primes then they become sexy prime quadruplets. Learn more about Sexy prime quadruplets

First 20: {5, 11, 17, 23}, {11, 17, 23, 29}, {41, 47, 53, 59}, {61, 67, 73, 79}, {251, 257, 263, 269}, {601, 607, 613, 619}, {641, 647, 653, 659}, {1091, 1097, 1103, 1109}, {1481, 1487, 1493, 1499}, {1601, 1607, 1613, 1619}, {1741, 1747, 1753, 1759}, {1861, 1867, 1873, 1879}, {2371, 2377, 2383, 2389}, {2671, 2677, 2683, 2689}, {3301, 3307, 3313, 3319}, {3911, 3917, 3923, 3929}, {4001, 4007, 4013, 4019}, {5101, 5107, 5113, 5119}, {5381, 5387, 5393, 5399}, {5431, 5437, 5443, 5449}

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If {p, p + 6, p + 12} are primes then they become sexy prime triplets. Learn more about Sexy prime triplets

First 20: {5, 11, 17}, {7, 13, 19}, {11, 17, 23}, {17, 23, 29}, {31, 37, 43}, {41, 47, 53}, {47, 53, 59}, {61, 67, 73}, {67, 73, 79}, {97, 103, 109}, {101, 107, 113}, {151, 157, 163}, {167, 173, 179}, {227, 233, 239}, {251, 257, 263}, {257, 263, 269}, {271, 277, 283}, {347, 353, 359}, {367, 373, 379}, {557, 563, 569}

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Primes of the form the form 2a ± 2b ± 1, where 0 < b < a. Learn more about Solinas primes

First 20: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 59, 61, 67, 71, 73, 79, 97

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Prime is Sophie Germain prime if it has form 2p + 1, where p is also a prime. Learn more about Sophie Germain primes

First 20: 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293

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Super-prime numbers are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. Learn more about Super primes

First 20: 3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, 211, 241, 277, 283, 331, 353

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Primes of the form Of the form 3×2^n − 1. Learn more about Thabit primes

First 9: 2, 5, 11, 23, 47, 191, 383, 6143, 786431

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Primes of the form Of the form 3×2^n + 1. Learn more about Thabit primes of the 2nd kind

First 7: 7, 13, 97, 193, 769, 12289, 786433

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If {p, p + 2} are primes then it becomes a prime twin. Learn more about Twin primes

First 20: {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}

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Prime which is left-truncatable prime and right-truncatable prime. Learn more about Two-sided primes

First 15: 2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397

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Primes in the Ulam sequence. Learn more about Ulam primes

First 20: 2, 3, 11, 13, 47, 53, 97, 131, 197, 241, 409, 431, 607, 673, 739, 751, 983, 991, 1103, 1433

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Primes of the form (2^n + 1)/3 where n is odd prime. Learn more about Wagstaff primes

First 7: 3, 11, 43, 683, 2731, 43691, 174763

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

First 5: 294001, 505447, 584141, 604171, 971767

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Primes that are also Wedderburn–Etherington numbers. Learn more about Wedderburn-Etherington primes

First 7: 2, 3, 11, 23, 983, 2179, 24631

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Wilson primes p is such that p^2 divides (p − 1)! + 1 Learn more about Wilson primes

First 3: 5, 13, 563

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Primes of the form n×2^n - 1. Learn more about Woodall primes

First 3: 7, 23, 383

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