Finding Large Primes

Gavriel Yarmish; Joshua Yarmish; Jason Yarmish

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arXiv · 1709.09963

Finding Large Primes

Gavriel Yarmish·Joshua Yarmish·Jason Yarmish

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Abstract

In this paper we present and expand upon procedures for obtaining large d digit prime number to an arbitrary probability. We use a layered approach. The first step is to limit the pool of random number to exclude numbers that are obviously composite. We first remove any number ending in 1,3,7 or 9. We then exclude numbers whose digital root is not 3, 6, or 9. This sharply reduces the probability of the random number being composite. We then use the Prime Number Theorem to find the probability that the selected number n is prime and use primality tests to increase the probability to an arbitrarily high degree that n is prime. We apply primality tests including Euler's test based on Fermat Little theorem and the Miller-Rabin test. We computed these conditional probabilities and implemented it using the GNU GMP library.

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Gavriel Yarmish, Joshua Yarmish, Jason Yarmish. 2017-09-25. Finding Large Primes. https://arxiv.org/abs/1709.09963

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