# Stern prime

If for a given prime number $q$ there is no smaller prime $p$ and nonzero integer $b$ such that $q=2b^{2}+p$, then $q$ is a Stern prime. These primes were first studied by Moritz Abraham Stern, in connection to a lesser known conjecture of Goldbach’s. Like other mathematicians of the time, Stern considered 1 to be a prime number. Thus his list of Stern primes read thus: 2, 17, 137, 227, 977, 1187, 1493. A century later the list has been amended to include 3 (as in A042978 of Sloane’s OEIS) but no terms larger than 1493 have been found. The larger of a twin prime is not a Stern prime.

Title Stern prime SternPrime 2013-03-22 16:19:10 2013-03-22 16:19:10 PrimeFan (13766) PrimeFan (13766) 4 PrimeFan (13766) Definition msc 11N05