So we can't use 7 in this reasoning. We quickly test odd multiples of 15 from 22 to 1035, and discover the three remaining known solutions. This is Imran's result, all other solutions must be a multiple of 165. By now you get the idea. This means we can look at all the primes up to 77 and see which ones match the condition.
M grows more slowly.
The test can be made very fast but that is still billions of tests. The gap to the next prime satisfying the condition, and the number of tests needed, grows bigger and bigger. Then there are infinite twin primes. Copyright 1999-2000 primepuzzles.net . All rights reserved.