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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) E. Rowland proved that if you set a(1) = 7, and for n > 2, a(n) = a(n1) + gcd(n,a(n1)); then a(n)  a(n1) (the "first differences") are all either 1 or prime. The list of prime generated by this formula begins 5, 3, 11, 3, 23, 3, 47, 3... (but it generates mostly 1s). [Caldwell]
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