Repdigits and repunits

A repdigit is a natural number with one repeating digit; the name, in fact, comes from the term “repeated digit.” The most famous redigit is the so-called “Beast Number” 666, a common symbol of the antichrist or of Satan. A repunit, then, is a repdigit that only uses the number 1; repunits pop up frequently in binary code and are related to that most famous of primes, Mersenne Primes. It has been conjectured that there are an infinite number of repunit primes, so if you’d like to try to prove it, please do so at your leisure.