99999999999999997

This number is a prime.

                                                          9999999 9999999997

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(99999999999999997, 100000000000000003) is the largest pair of sexy primes less than a googol of form (k*10^n-3, k*10^n+3), (case k=1, n=17). The smaller such pair is (1997, 2003), (case k=2, n=3). [Loungrides]