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We introduce and consider a certain probability question involving elementarynumber theory and the likelihood that a fixed prime will appear in a certainrecursively defined factorization of an integer. We derive several convergentinfinite products for this probability, which we are unable to simplify toobtain closed form solutions. However, we are able to implement these formulasin the development of algorithms to obtain arbitrarily close rigorous bounds onthe probabilities in question.

Primes Appearing in Prime Tower Factorization