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A surprising prime gap (Posted on 2016-07-27) Difficulty: 3 of 5
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?

See The Solution Submitted by Math Man    
Rating: 5.0000 (1 votes)

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re: My solution | Comment 4 of 8 |
(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 2016-07-30 20:37:42
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