Let a prime number generated by Euler's prime-generating polynomial n^2 + n + 41 be known as an Euler prime. (Note that such primes are distinct from prime Euler numbers, which are known here as Euler number primes). Then the first few Euler primes occur for n = 1, 2, ..., 39, 42, 43, 45, ... (OEIS A056561), corresponding to the primes 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, ... (OEIS A005846). As of Feb. 2013, the largest known Euler prime is 1523844527...6354845061, which has 398204 decimal digits and was found by D. Broadhurst (http://primes.utm.edu/primes/page.php?id=111195).

Eulerian number | Euler number | Euler number prime | integer sequence primes | prime-generating polynomial

Leonhard Euler