Several other theorems were proved concerning prime numbers. many great mathematicians approached problems that are related to primes. There are still many open problems of which we will mention some.
Conjecture 1. Twin Prime Conjecture There are in?nitely many pairs primes p and p + 2.
Conjecture 2. Goldbach's Conjecture Every even positive integer greater than 2 can be written as the sum of two primes.
Conjecture 3. The n2 + 1 Conjecture There are in?nitely many primes of the form n2 + 1, where n is a positive integer.
Conjecture 4. Polignac Conjecture For every even number 2n are there infinitely many pairs of consecutive primes which differ by 2n.
Conjecture 5. Opperman Conjecture Is there always a prime between n^2 and
(n + 1)^2?