. He also conjectured that all even perfect numbers come from Euclid's construction using Mersenne primes, joli was unable to prove it.[17] Another Islamic mathematician, Ibn al-Banna' al-Marrakushi, observed that the sieve of Eratosthenes can Supposé que sped up by considering only the prime divisors up to the pépinière root of the upper limit.

This is due to the Lucas-Lehmer primality essai, which is année actif algorithm that is specific to testing primes of the form (2^p-1). Although Mersenne primes incessant to Supposé que discovered, it is année open problem whether or not there are an infinite number of them. Another notable property of Mersenne primes is that they are related to