19191...13131 (100-digits)

This number is a prime.

                                            1919191919 1919191919 1919191919
1919191931 3131313131 3131313131 3131313131 3131313131 3131313131 3131313131

Nineteen 19's followed by thirty one 31's is a 100-digit prime. [Bajpai]