3

This number is a prime.

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Jason Funk © 2002

The product of the smaller in a set of twin primes (3), the next integer (4), and the larger twin (5), equals 60, which falls between another set of twin primes {59, 61}. In other words, {p, p+2} and {p*(p+1)*(p+2)-1, p*(p+1)*(p+2)+1} are two sets of twin primes, where p is prime (smallest case p=3), i.e., {3,5} and {59,61}. Can you find the smallest prime p where this occurs recursively for 3 sets? 4 sets? 5 sets? etc. The sequence begins 3, 53137619, 2856646544865959, ... . [Honaker]