# List of primes by type

 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+1 Of the form . Form 4n+1 Of the form . Form 4n+3 Of the form . Emirp Reversible primes Euler prime numbers Of the form . Mersenne primes Of the form . Euclid primes Of the form . Primorial primes Of the form . Fermat primes Of the form . Factorial primes Of the form n! − 1 or n! + 1 . Double factorial primes Of the form n!! − 1 or n!! + 1 . Sophie Germain primes p and 2p + 1 are both prime . Safe primes p and (p - 1) / 2 are both prime . Left-truncatable primes Right-truncatable primes Two-sided primes Wilson primes p2 divides (p − 1)! + 1 . Super primes p-th prime Odd primes Of the form .