Primes Appearing in Prime Tower Factorization

Details Primes Appearing in Prime Tower Factorization Primes Appearing in Prime Tower Factorization

2012-04-24

arxiv.org/abs/1204.5251v1

Mathematics

Number Theory

First draft

Scientific paper

We introduce and consider a certain probability question involving elementary number theory and the likelihood that a fixed prime will appear in a certain recursively defined factorization of an integer. We derive several convergent infinite products for this probability, which we are unable to simplify to obtain closed form solutions. However, we are able to implement these formulas in the development of algorithms to obtain arbitrarily close rigorous bounds on the probabilities in question.

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