Number Theory

    

Two Conjectures on the Numbers Obtained Concatenating the Squares of Two Primes Q and R Where R = Q+18n

Authors: Marius Coman

In this paper I state the following two conjectures: (I) For any prime q greater than 5 there exist an infinity of primes p obtained subtracting the square of q or the square of r from the number obtained concatenating the square of q with the square of r, where r prime, r = q + 18*n, and adding 1 (for example, p = 121841 – 121 + 1 = 121721, prime, also p = 121841 – 841 + 1 = 121001, prime, where q^2 = 11^2 = 121, r^2 = 29^2 = 841 and 29 = 11 + 18*1); (II) For any positive integer n there exist an infinity of triplets of primes [p, q, r] such that r = q + 18*n and p is obtained subtracting the square of q or the square of r from the number obtained concatenating the square of q with the square of r and adding 1.

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[v1] 2016-03-12 05:31:28

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