77

This number is a composite.

There are 77 primes that never enter the repdigit sequence 1, 31, 331, 3331, 33331, etc. as factors. The sequence has general n-th term s(n) = (10^n-7)/3 and the primes correspond to n = 3, 5, 7, 11, 13, 37, 41, 43, 53, 61, 67, 71, 73, 79, 89, 101, 103, 107, 127, 137, 139, 151, 157, 163, 173, 191, 211, 239, 241, 251, 271, 277, 281, 293, 317, 347, 349, 359, 397, 409, 443, 449, 457, 521, 547, 599, 601, 613, 617, 631, 641, 643, 677, 683, 691, 733, 739, 751, 757, 761, 769, 773, 797, 827, 853, 859, 881, 883, 907, 911, 919, 929, 947, 967, 991 and 997. [Schiffman]