By formula
[[Fermat number|Fermat (22n + 1 )]]
[[Mersenne prime|Mersenne (2p − 1 )]]
[[Double Mersenne number|Double Mersenne (22p −1 − 1 )]]
[[Wagstaff prime|Wagstaff (2p + 1)/3 ]]
[[Proth prime|Proth (k ·2n + 1 )]]
[[Factorial prime|Factorial (n ! ± 1 )]]
[[Primorial prime|Primorial (pn # ± 1 )]]
[[Euclid number|Euclid (pn # + 1 )]]
[[Pythagorean prime|Pythagorean (4n + 1 )]]
[[Pierpont prime|Pierpont (2m ·3n + 1 )]]
[[Quartan prime|Quartan (x 4 + y 4 )]]
[[Solinas prime|Solinas (2m ± 2n ± 1 )]]
[[Cullen number|Cullen (n ·2n + 1 )]]
[[Woodall number|Woodall (n ·2n − 1 )]]
[[Cuban prime|Cuban (x 3 − y 3 )/(x − y )]]
[[Leyland number|Leyland (xy + yx )]]
[[Thabit number|Thabit (3·2n − 1 )]]
[[Williams number|Williams ((b −1)·b n − 1 )]]
[[Mills' constant|Mills (⌊ A 3n ⌋ )]]
By integer sequence By property Base -dependentPatterns
[[Twin prime|Twin (p , p + 2 )]]
[[Bi-twin chain|Bi-twin chain (n ± 1, 2n ± 1, 4n ± 1, … )]]
[[Prime triplet|Triplet (p , p + 2 or p + 4, p + 6 )]]
[[Prime quadruplet|Quadruplet (p , p + 2, p + 6, p + 8 )]]
k -tuple
[[Cousin prime|Cousin (p , p + 4 )]]
[[Sexy prime|Sexy (p , p + 6 )]]
Chen
[[Safe and Sophie Germain primes|Sophie Germain/Safe (p , 2p + 1 )]]
[[Cunningham chain|Cunningham (p , 2p ± 1, 4p ± 3, 8p ± 7, ... )]]
[[Primes in arithmetic progression|Arithmetic progression (p + a·n , n = 0, 1, 2, 3, ... )]]
[[Balanced prime|Balanced (consecutive p − n , p , p + n )]]
By size Complex numbers Composite numbers Related topics First 60 primes
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