Number Theory

    

Primes Obtained Concatenating P Prime with P+2 and P+6 Respectively with P+4 and P+6

Authors: Marius Coman

The triplets of primes [p, p + 2, p + 6] and [p, p + 4, p + 6] have already been studied: Hardy and Wright conjectured that there exist an infinity of such triplets. In this paper I make the following two conjectures on the triplets [p, p + 2, p + 6] and [p, p + 4, p + 6], but only p is required to be prime: (I) there exist an infinity of primes q obtained concatenating a prime p with p + 2 then with p + 6; example: for p = 11, the number q = 111317 is prime; (II) there exist an infinity of primes q obtained concatenating a prime p with p + 4 then with p + 6; example: for p = 241, the number q = 241245247 is prime.

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[v1] 2016-04-04 12:03:24

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