A repunit is a number using only one digit. The numbers 11 and
1111111111111111111 are examples of repunit primes. The number
of ones in such a repunit primes can be 2, 19, 23, 317, 1031,
49081, 86453, or 109297. An almost repunit number repeats a
digit but one digit is different, for example, 222222922. The
primes of this form make interesting patterns, as shown in this
Demonstration. Whether there is any pattern to these is an
unsolved problem.