10000...00001 (10000-digits)

This number is a prime.

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]