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10000...00001 (10000-digits) (another Prime Pages' Curiosity) |
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits) 
This prime is the sum of the 8th powers
of integers with 1250 and 1112 digits, namely
N=(28*x^9-2*x)^8+(32*x^8-1)^8, where
x=5*17*24135542731*164430412448406653*15351348188298712888796082898266183649073690205237660009696003540868926490197736695774128091808423365118301699
is completely factorized into proven primes.
Since N-1 is divisible by 5*(2*x^2)^12, which exceeds
the cube root of N, the primality of N may be proven
by the methods of Brillhart, Lehmer and Selfridge. [Broadhurst and
Twain]
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