Smooth number

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An integer is S-smooth if it does not contain any prime factors less than or equal to S. The relevance of this concept to the finding primes project is that if one inserts a non-S-smooth number into a factoring oracle, one will obtain a prime of size greater than S. So it would suffice to find a small (and enumerable) set which is guaranteed to contain at least one non-S-smooth number for some large S.