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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The largest known prime Lucas number to have a composite index. [Dobb] Largest known prime of the sequence a(0) = 3; thereafter, a(n) = a(n1)^2  2. We start with the prime 3. Then 3^22 = 7 is prime. Next 7^22 = 47 is prime. Finally, 47^22 = 2207 is prime. [Post] The largest number in a Collatz trajectory is 250504 for 2207 different numbers. [Gaydos] If you type 2, 2, 0, 7, √, √, √, √ (i.e., repeat the square root of 2207 four times) on a calculator you'll get a good approximation of the golden ratio (phi). [Petrov]
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