The prime distance pd(n) of a nonnegative integer n is the absolute difference between n and the nearest prime. It is therefore true that pd(p) = 0 for primes p. The first few values for n = 0, 1, 2, ... are therefore 2, 1, 0, 0, 1, 0, 1, 0, 1, 2, ... (OEIS A051699). The values of n having prime distances of 0, 1, 2, 3, ... are 2, 1, 0, 26, 93, 118, 119, 120, 531, 532, 897, ... (OEIS A077019).

nearest prime | prime difference function | prime gaps