The infinitude of such numbers was proven by Euclid in his Elements.
Robert Carmichael names the set of false-positives in testing for this. Distributed asymptotically, a random number near a large number N has about a one over natural log of N chance of having it. Landau's problems, two of which are the Legendre and Goldbach conjectures, concern this property. Most algorithmic tests for this property are probabilistic, such as the Miller-Rabin test. The Sieve of Atkin is an optimized method of computing numbers with this property, based on the ancient Sieve of Eratosthenes. The infinitude of such numbers was proven by Euclid in his Elements. For 10 points, name this property of natural numbers with exactly two divisors, itself and one.
Robert Carmichael names the set of false-positives in testing for this.
{prime} number or {primality} (accept word forms)