# 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.

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, 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, 284743: 15

## Prime Number Types#

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

### Additive 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.

### Bell prime#

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

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

### Carol prime#

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.

### Centered decagonal prime#

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.

### Centered heptagonal prime#

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.

### Centered square prime#

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.

### Centered triangular prime#

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.

### Chen prime#

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.

### Class 1+ prime#

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.

### Cousin prime#

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.

### Cuban prime 1#

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.

### Cuban prime 2#

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.

### Cullen prime#

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.

### Dihedral prime#

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.

### Double mersenne prime#

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

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

### Emirps#

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.

### Euclid prime#

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.

### Factorial prime#

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.

### Fermat prime#

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

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

### Fibonacci prime#

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.

### Genocchi prime#

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.

### Good prime#

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.

### Happy prime#

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.

### Harmonic prime#

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.

### Isolated prime#

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.

### Kynea prime#

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.

### Left-truncatable prime#

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.

### Leyland prime#

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

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

### Long prime#

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.

### Lucas prime#

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.

### Lucky prime#

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.

### Mersenne prime#

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.

### Mills prime#

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

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

### Multiplicative prime#

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.

### Palindromic prime#

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.

### Pierpont prime#

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.

### Pierpont prime of the 2nd kind#

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.

### Prime#

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.

### Prime quadruplet#

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.

### Prime quintuplet 1#

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.

### Prime quintuplet 2#

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.

### Prime sextuplet#

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.

### Prime triplet#

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.

### Proth prime#

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.

### Pythagorean prime#

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.

### Quartan prime#

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.

### Restricted left-truncatable prime#

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.

### Restricted right-truncatable prime#

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.

### Right-truncatable prime#

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.

### Safe prime#

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.

### Semiprime#

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.

### Sexy prime#

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.

### Sexy prime quadruplets#

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}

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

Checkout sexy prime quadrupletss up to: 100, 500, 1000, 10000.

### Sexy prime triplet#

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}

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

### Solinas prime#

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

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

### Sophie germain prime#

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

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

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

### Super prime#

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

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

### Thabit prime#

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

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

### Thabit prime of the 2nd kind#

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

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

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

### Twin prime#

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}

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

### Two-sided prime#

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

Checkout list of first: 10, 50 two-sided primes. You can also check all two-sided primes.

### Ulam prime#

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

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

### Wagstaff prime#

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

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

### Weakly prime#

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

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

### Wedderburn-etherington prime#

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

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

Checkout list of first: 10 wedderburn-etherington primes. You can also check all wedderburn-etherington primes.

Checkout wedderburn-etherington primes up to: 100, 500, 1000, 10000.

### Wilson prime#

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

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

### Woodall prime#

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

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