The book is now available! 25475...67041 (6716-digits)
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

+ The generalized repunit (6750651153 - 1)/675064 is prime.

A proof is possible because of the remarkable circumstance that, for b = 5*37*41*89 and p = 27*32+1, both Phi(p,b) and Phi(p-1, b) are prime, where Phi(n, x) is the nth cyclotomic polynomial in x. [Broadhurst]

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