11111...11111 (104-digits)

This number is a prime.

                                       1111 1111111111 1111111111 1111111111
1111111111 1111111111 0111111111 1111111111 1111111111 1111111111 1111111111

+ The smallest anti-Yarborough near-repunit prime greater than a googol. [Loungrides]

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