Famously subject of a proof by Euclid showing that there are infinitely many numbers with this property, numbers that do not have this property are called composite.
This property is possessed by the constant described in Mills' theorem, and a one way of determining this property is by the Lucas-Lehmer test. A statement about the asymptotic incidence of this property is this property's namesake theorem, and the fact that every number can be written as the sum of two numbers with this property is given as Goldbach's conjecture. Famously subject of a proof by Euclid showing that there are infinitely many numbers with this property, numbers that do not have this property are called composite. For 10 points, name this property of a number that means it is divisible only by one and itself.
This property is possessed by the constant described in Mills' theorem, and a one way of determining this property is by the Lucas-Lehmer test.
{primality} [or {prime}]