# Primes By Type

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.

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### Bell prime#

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.

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### Carol prime#

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

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

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### Centered decagonal prime#

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.

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### 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.

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### Centered square prime#

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.

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### 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.

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### 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.

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### 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.

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### Cousin prime#

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

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### Cuban prime 1#

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

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### Cuban prime 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.

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### Cullen prime#

First 1: 3

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

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### Dihedral prime#

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.

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### 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

First 2: 7, 127

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### 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

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### 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.

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### Factorial prime#

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

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

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### Fermat prime#

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

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

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### Fibonacci prime#

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.

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### Genocchi prime#

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.

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### 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.

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### Harmonic prime#

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.

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### Isolated prime#

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.

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### Kynea prime#

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

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

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### 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.

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### Leyland prime#

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.

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### 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.

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### Lucas prime#

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.

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### 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.

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### Mersenne prime#

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

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

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### Mills prime#

First 3: 2, 11, 1361

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

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### Multiplicative prime#

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.

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### 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.

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### Pierpont prime#

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.

### 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

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### 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

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### 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

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### 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

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

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### 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

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### 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.

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### Pythagorean prime#

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.

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### 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.

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### 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.

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### 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.

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### 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.

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### 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.

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### 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.

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### Sexy prime#

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

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

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

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### Sexy prime triplet#

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

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

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### 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.

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### 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.

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### 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.

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### Thabit prime#

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.

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### 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.

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### Twin prime#

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

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### Two-sided prime#

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.

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### Ulam prime#

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.

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### 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.

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### 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.

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### Wedderburn-etherington prime#

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.

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### Wilson prime#

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

First 3: 5, 13, 563

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

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