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2016•viXraOpen access

Four conjectures on the triplets [p, p+4, p+10] and [p, p+6, p+10] where p prime

Marius Coman

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Abstract

In this paper I make the following four conjectures on the triplets [p, p + 4, p + 10] and [p, p + 6, p + 10]: (I) there exist an infinity of triplets of primes of the form [p, p + 4, p + 10]; (II) there exist an infinity of triplets of primes of the form [p, p + 6, p + 10]; (III) there exist an infinity of primes q obtained concatenating a prime p with p + 4 then with p + 10 (only p is necessary prime); (IV) there exist an infinity of primes q obtained concatenating a prime p with p + 6 then with p + 10 (only p is necessary prime).

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What this paper is about

In this paper I make the following four conjectures on the triplets [p, p + 4, p + 10] and [p, p + 6, p + 10]: (I) there exist an infinity of triplets of primes of the form [p, p + 4, p + 10]; (II) there exist an infinity of triplets of primes of the form [p, p + 6, p + 10]; (III) there exist an infinity of primes q obtained concatenating a prime p with p + 4 then with p + 10 (only p is necessary prime); (IV) there exist an infinity of primes q obtained concatenating a prime p with p + 6 then with p + 10 (only p is necessary prime).

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Available abstract

In this paper I make the following four conjectures on the triplets [p, p + 4, p + 10] and [p, p + 6, p + 10]: (I) there exist an infinity of triplets of primes of the form [p, p + 4, p + 10]; (II) there exist an infinity of triplets of primes of the form [p, p + 6, p + 10]; (III) there exist an infinity of primes q obtained concatenating a prime p with p + 4 then with p + 10 (only p is necessary prime); (IV) there exist an infinity of primes q obtained concatenating a prime p with p + 6 then with p + 10 (only p is necessary prime).

Key concepts: Infinity, Prime (order theory), Mathematics, Combinatorics, Prime number, Mathematical analysis

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Four conjectures on the triplets [p, p+4, p+10] and [p, p+6, p+10] where p prime — Research Paper | ScholarLens