Determine the possible nonzero units digits of a duodecimal positive integer n such that:

Each of n and n+2 is a prime number, and:

n+2 is expressible as the sum of squares of two positive itegers.

(In reply to heuristic computer exploration -- no proof by Charlie)

Actually there are 19,289 such pairs that had been checked up through and including the pair 6104927, 6104929. The program had missed a few by checking for sums of squares only up to int(sqrt(N)/2) as the smaller one instead of int(sqrt(N/2)).

They all still check out with the same last duodecimal digit and the confirmation is stronger than before.
 

Posted by Charlie on 2011-09-22 21:38:05