A theorem named for them, which was proved by de la Vallee Poussin and Hadamard, describes their distribution.
These constructs have arbitrarily long arithmetic progressions according to the Green-Tao theorem. Yitang Zhang used the Bombieri-Vinogradov theorem in a recent paper concerning bounded gaps between these entities. Euler discovered a quadratic polynomial that generates these entities, which are visible on the Ulam spiral. A theorem named for them, which was proved by de la Vallee Poussin and Hadamard, describes their distribution. The difficulty in factoring them is the basis of RSA cryptography, and they can be obtained using the sieve of Eratosthenes. For 10 points, name these numbers that are only divisible by one and themselves.
These constructs have arbitrarily long arithmetic progressions according to the Green-Tao theorem.
 prime numbers [or primes] 