8237

This number is a prime.

The integer sequence generated by the recurrence a(n) = a(n-1) + 2^a(n-2) starts 1, 1, 3, 5, 13, 45, 8237..., and 8237 is prime. In fact, 8237 is the last known prime in this sequence, since the next term, 35184372097069, is composite and and the term after that (which has 2480 digits) is also composite. The next term after that has approximately 10.6 trillion digits and its prime status is not known. [Keith]