8779

This number is a prime.

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8779 is the largest prime factor of the number 100000000001 (= 10^11 + 1), whose complete factorization is 11 x 11 x 23 x 4093 x 8779. Only three four-digit primes are the largest prime factor of 10^n + 1 for some n; the other two are 9091 (for both n=5 and n=15) and 9901 (for n=6). [Keith]