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?
I looked at a list of record prime gaps. Every number below 16 fit in an all composite row smaller than the smallest gap which might have fit the next row. Fox example rows of N=6 fit in the prime gap of 7 composites after 89 so I didn't have to check if they filled the next record gap of 13 composites after 113.
The N=16 rows do not fit in any of the record gaps before the 33 composites after 1327. And there is room for two consecutive rows.
But I was unable to confirm that there is a non-record but still large gap that a row might have otherwise fit - this would have invalidated the solution.
The big question is whether 16 is unique as the wording of the problem seems to suggest.
Posted by Jer
on 2016-07-27 18:05:19