Number Theory


Conjecture on Numbers N Obtained Concatenating Two Primes Related to the Number of Primes up to N

Authors: Marius Coman

In this paper I conjecture that there exist an infinity of numbers n obtained concatenating two primes p and q, where p = 30*k + m1 and q = 30*h + m2, p < q, m1 and m2 distinct, having one from the values 1, 7, 11, 13, 17, 19, 23, 29, such that the number of primes congruent to m1 (mod 30) up to n is equal to the number of primes congruent to m2 (mod 30) up to n. Example: for n = 1723 obtained concatenating the primes p = 17 and q = 23, there exist 34 primes of the form 30*k + 17 up to 1723 and 34 primes of the form 30*k + 23 up to 1723.

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[v1] 2016-12-29 16:06:30

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