8191

This number is a prime.

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+ Each term in the sequence of primes 7, 89, 5591, 3851459, ..., has a Mersenne prime number of consecutive composites that follow them. Can you find a prime that is followed by a gap of 8191 consecutive composites? (Someday, someone will find its first occurrence!) [Honaker]

+ 8191 is a Fibonacci 13-step number. Note that 2^13-1 = 8191, making it a Mersenne prime also. Will Mersenne primes continue to appear in this way? [Loungrides and Honaker]

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