Euler’s lucky number

A prime numberMathworldPlanetmath p is one of Euler’s lucky numbers if n2-n+p for each 0<n<p is also a prime. Put another way, a lucky number of EulerMathworldPlanetmath’s plus the nth oblong number produces a list of primes p-long. There are only six of them: 2, 3, 5, 11, 17 and 41, these are listed in A014556 of Sloane’s OEIS.

41 is perhaps the most famous of these. We can verify that 2 + 41 is 43, a prime, that 47 is also prime, so are 53, 61, 71, 83, 97, and so on to 1601, giving a list of 41 primes. Predictably, 1681 is divisible by 41, being its square. For n>p the formula does not consistently give only composites or only primes.

Title Euler’s lucky number
Canonical name EulersLuckyNumber
Date of creation 2013-03-22 16:55:33
Last modified on 2013-03-22 16:55:33
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 4
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A41
Synonym lucky number of Euler
Synonym Eulerian lucky number