| viXra.org > Number Theory > viXra:1603.0367 |
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| viXra.org > Number Theory > viXra:1603.0367 |
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Number Theory |
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Authors: Marius Coman
In this paper I make the following two conjectures: (I) For any prime p, p > 5, there exist a pair of primes (q1, q2), both having the group of their last digits equal to p, and a positive integer n, such that p = (n + 1)*q1 – n*q2 (examples: for p = 11, there exist the primes q1 = 211 and q2 = 311 and also the number n = 2 such that 11 = 3*211 – 2*311; for p = 29, there exist the primes q1 = 829 and q2 = 929 and also the number n = 8 such that 29 = 9*829 – 8*929); (II) For any q1 prime, q1 > 5, and any n non-null positive integer, there exist an infinity of primes q2, having the group of their last digits equal to q1, such that p = (n + 1)*q2 – n*q1 is prime; (III) For any q1 prime, q1 > 5, and any q2 prime having the group of its last digits equal to q1, there exist an infinity of positive integers n such that p = (n + 1)*q2 – n*q1 is prime.
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[v1] 2016-03-27 04:47:03
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