2016Unpublished venueOpen access

Four conjectures on the numbers p±1 concatenated with 1 where p primes of the form 30k+11

Marius Coman

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Abstract

In this paper I state the following four conjectures. Let q be the number obtained concatenating to the right with 1 the numbers p – 1, where p primes of the form 30*k + 11; then: (I) there exist an infinity of primes q; (II) there exist an infinity of semiprimes q = q1*q2, such that q2 + q1 - 1 is prime. Let q be the number obtained concatenating to the right with 1 the numbers p + 1, where p primes of the form 30*k + 11; then: (III) there exist an infinity of primes q; (IV) there exist an infinity of semiprimes q = q1*q2, such that q2 – q1 + 1 is prime.

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What this paper is about

In this paper I state the following four conjectures. Let q be the number obtained concatenating to the right with 1 the numbers p – 1, where p primes of the form 30*k + 11; then: (I) there exist an infinity of primes q; (II) there exist an infinity of semiprimes q = q1*q2, such that q2 + q1 - 1 is prime. Let q be the number obtained concatenating to the right with 1 the numbers p + 1, where p primes of the form 30*k + 11; then: (III) there exist an infinity of primes q; (IV) there exist an infinity of semiprimes q = q1*q2, such that q2 – q1 + 1 is prime.

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Available abstract

In this paper I state the following four conjectures. Let q be the number obtained concatenating to the right with 1 the numbers p – 1, where p primes of the form 30*k + 11; then: (I) there exist an infinity of primes q; (II) there exist an infinity of semiprimes q = q1*q2, such that q2 + q1 - 1 is prime. Let q be the number obtained concatenating to the right with 1 the numbers p + 1, where p primes of the form 30*k + 11; then: (III) there exist an infinity of primes q; (IV) there exist an infinity of semiprimes q = q1*q2, such that q2 – q1 + 1 is prime.

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

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