- Cullen (4)
- The Cullen numbers Cn=n.2n+1 are named after Reverend Cullen because of a question he posed in 1905.
- Cunningham chains (6)
- Chains of primes where each is the preceeding prime doubled plus one or
doubled minus one.
- Fermat (4)
- The Fermat numbers are the numbers of the form 22n+1. They are prime for n = 0, 1, 2, 3 and 4. But little is known for larger values of n.
- Mersenne (9)
- The Mersenne primes are primes of the form 2p-1 where p is a prime number. These are usually the largest known prime and are certainly the most studied.
- Sierpinski (2)
- Primes found in the effort to decide the Sierpinski problem: is 78557 the least odd integer k for which the integers k.2n+1 are all composite?
- Sophie Germain (1)
- Sophie Germain Prime are the primes p such that 2p+1 is also prime.
- Woodall (6)
- The Woodall numbers are those of the form Wn=n.2n-1. These are sometimes called the Cullen numbers (of the second kind).
- near products (7)
- Primorial, factorial, multifactorial, deficient factorials...
- other searches (3)
- Organized searches for primes that do not fit in one of the special forms listed.
- palindrome (4)
- Palindrome read the same forward and backwards. The first few palindromic primes are 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, ...