11111...11111 (38-digits)

This number is a composite.

                                   11111111 1111111111 1111111111 1111111111

This repunit has the unique property of having only unique primes (11, (10^19-1)/9 and (10^19+1)/11) as factors. Such a number could only occur for a prime where both (10^p-1)/9 and (10^p+1)/11 were prime. It is unlikely any prime except 19 has that property.