List of primes by type

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Twin primes(p, p + 2) are both prime.
Prime triplets(p, p + 2, p + 6) or (p, p + 4, p + 6) are all prime.
Prime quadruplets(p, p + 2, p + 6, p + 8) are all prime.
Cousin primes(p, p + 4) are both prime.
Sexy primes(p, p + 6) are both prime.
Form 3n+1Of the form 3n + 1 .
Form 4n+1Of the form 4n + 1 .
Form 4n+3Of the form 4n + 3 .
EmirpReversible primes
Euler prime numbersOf the form n^2 + n + 41 .
Mersenne primesOf the form 2^n - 1 .
Euclid primesOf the form p_n# + 1 .
Primorial primesOf the form p_n# \pm 1 .
Fermat primesOf the form 2^2^n + 1 .
Factorial primesOf the form n! − 1 or n! + 1 .
Double factorial primesOf the form n!! − 1 or n!! + 1 .
Sophie Germain primesp and 2p + 1 are both prime .
Safe primesp and (p - 1) / 2 are both prime .
Left-truncatable primes
Right-truncatable primes
Two-sided primes
Wilson primesp2 divides (p − 1)! + 1 .
Super primesp-th prime
Odd primesOf the form 2n - 1 .
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