N is a positive integer. If you list the positive integers in rows of N such that the first row contains 1 to N, the second row contains N+1 to 2*N, and so on, then the first row with no prime is immediately followed by another row with no prime. What is N?
(In reply to
My solution by Jer)
16 is probably the unique solution. The minimum length prime gap to contain 2 rows ending at multiples of N has length 2*N+2. When N is large, there will be many gaps containing 1 row before there is a gap containing 2 rows. The prime gap from 1327 to 1361 is very surprising. It has length 34=2*16+2, and it is at the perfect position to contain 3 multiples of 16. Also, no gap before that contains more than 1 multiple of 16.

Posted by Math Man
on 20160730 20:37:42 