# Prime number

There are many particular types of primes:

>> Primes of the form 2^p − 1, where

*p*is a prime number, are known as Mersenne primes.>> Primes of the form 2^{2^k} + 1 are Fermat primes.

>> Prime numbers

*p*where 2*p*+ 1 is also prime are known as Sophie Germain primes.I'm particularly interested in prime numbers of the forms (4k + 1) and (4k + 3).

Primes of the form (4k + 1) can be expressed as the sum of two squares, and prime numbers of the form (4k + 3) can be expressed as the sum of four squares.

We can find a number, a, such that a^2 = -1 (mod p), where p is a prime of the form 4k+1

And, I'm also interested in prime numbers p such that exactly one of the numbers 2p-1 and 2^p - 1 is prime.

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