User blog:ArtismScrub/1111

(a "binary number" in this context is a number that only contains 0s and 1s in its decimal expansion.)

1111's prime factorization is 11 * 101.

I firmly believe it is the only base 10 non-prime repunit number whose prime factorization consists of only binary numbers, making it a special binary number. I've tested this up to 11,111, 111,11 1,111,1 11,111, 111,11 1,111,1 11,111, 111,11 1,111,1 11,111 (that's 50 digits) and all other results have given non-binary numbers. Since the odds of each repunit having this property decreases the larger it gets, this seems to be a solid conjecture.

I am not entirely sure about non-repunit binary numbers, nor am I sure about repunits in other numeral bases. I doubt this is the only base 10 binary number that has this property.

This isn't a super-large number thing, no. Just an interesting numerical property I found on my own, and nobody else seems to have acknowledged, judging by a quick search, and I dunno where else I could submit this.