You might want to look into "repunits" (though we really do want the 9s, actually) and the Cunningham Project. Mersenne primes, the largest known, are the base

You might want to look into "repunits" (though we really do want the 9s, actually) and the Cunningham Project. Mersenne primes, the largest known, are the base-2 case of these (in which case there is no "9"s distinction).