Any fraction with a prime in the denominator would start its own series..........and would never be contained in another fraction's geo series..............I bet Euler got his idea like that.........which was mentioned in the book..........."Music of the Primes"......

Something else strange about doing that jumped out at me..............................b/c the 2nd set of ten fractions......................from 1/10 to 1/20 contain more original geo series than the 1st ten..........counter intuitive...............b/c one would usually reason that the higher the number...........the less chance it has to be original............b/c another number would seem to multiply up to it...........



“Nonsense, you gullible old toad!” you are perhaps shouting to your screen. “Why should throwing out the numbers with 9’s make such a difference? We’ve still got all the other numbers!”