Conjecture   Every even number greater than can be represented as the sum of an odd prime number and an odd semiprime .

Conjecture   Polignac's Conjecture: For any positive even number n, there are infinitely many prime gaps of size n. In other words: There are infinitely many cases of two consecutive prime numbers with difference n.

Conjecture   Twin Prime Conjecture: There are an infinite number of twin primes.

Conjecture   If every second positive integer except 2 is remaining, then every third remaining integer except 3, then every fourth remaining integer etc. , an infinite number of the remaining integers are prime.

Conjecture   There exist infinitely many positive integers so that both and are prime.

Conjecture   For any prime , there exists a Fibonacci number divisible by exactly once.

Conjecture   For any prime , does not divide where is the Legendre symbol.

Conjecture   Every even integer greater than 2 is the sum of two primes.