11111...11111 (37-digits)

This number is a prime.

                                    1111114 1111444411 4241144441 1114111111

             1
            1 1
       1 1 1 4 1 1 1
        1 4 4 4 4 1
         1 4 2 4 1
        1 4 4 4 4 1
       1 1 1 4 1 1 1
            1 1
             1

The smallest star-congruent prime of order 3. If we concatenate the number of digits in each row, i.e., 1, 2, 7, 6, 5, 6, 7, 2, 1, we form another palindromic prime. [Honaker]