This article defines a property that can be evaluated for a prime number. In other words, every prime number either satisfies this property or does not satisfy this property.
View other properties of prime numbers | View other properties of natural numbers
It turns out that if is prime, then itself is also prime, though the converse is not true (the smallest counterexample is , because ).
Facts in number theory
- Mersenne number is prime implies number is prime
- Mersenne number for prime or Poulet implies prime or Poulet
Facts in other branches of mathematics
The Mersenne numbers are prime for , with the corresponding primes being . Them smallest prime for which the Mersenne number is not prime is : .
Further information: Infinitude conjecture for Mersenne primes
It is conjectured that there are infinitely many Mersenne primes.