11111...11111 (319-digits)

This number is a probable-prime (likely to be a prime but we have not (re-)proven it on this site).

                                  111111111 1111111111 1111111111 1111111111
1111111111 1111101111 1111111111 1111111111 1111111111 1111111111 1111111111
1111111111 1111111111 1111111111 1111111111 1111111111 1111111111 1111111111
1111111111 1111111111 1111111111 1111111111 1111111111 1111111111 1111111111
1111111111 1111101111 1111111111 1111111111 1111111111 1111111111 1111111111

The largest non-titanic palindromic prime formed by sandwiching two zeros between the digits of a repunit prime, i.e., R₃₁₇. Note that the smallest such prime is 111111110111011111111. [Loungrides]