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Conjecture on the Infinity of Primes Obtained Concatenating a Prime P with P+30k

Marius Coman

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Abstract

In this paper I make the following conjecture: for any p prime, p > 5, there exist an infinity of k positive integers such that the number q obtained concatenating to the right p with p + 30*k is prime (examples: for p = 13, the least k for which q is prime is 2 because 1373 is prime; for p = 104729, the least k for which q is prime is 3 because 104729104819 is prime). It is notable the small values of k for which primes q are obtained, even in the case of primes p having 20 digits, so this formula could be a way to easily find, starting from a prime p, a prime q having twice as many digits!

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What this paper is about

In this paper I make the following conjecture: for any p prime, p > 5, there exist an infinity of k positive integers such that the number q obtained concatenating to the right p with p + 30*k is prime (examples: for p = 13, the least k for which q is prime is 2 because 1373 is prime; for p = 104729, the least k for which q is prime is 3 because 104729104819 is prime). It is notable the small values of k for which primes q are obtained, even in the case of primes p having 20 digits, so this formula could be a way to easily find, starting from a prime p, a prime q having twice as many digits!

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Available abstract

In this paper I make the following conjecture: for any p prime, p > 5, there exist an infinity of k positive integers such that the number q obtained concatenating to the right p with p + 30*k is prime (examples: for p = 13, the least k for which q is prime is 2 because 1373 is prime; for p = 104729, the least k for which q is prime is 3 because 104729104819 is prime). It is notable the small values of k for which primes q are obtained, even in the case of primes p having 20 digits, so this formula could be a way to easily find, starting from a prime p, a prime q having twice as many digits!

Key concepts: Prime (order theory), Mathematics, Infinity, Conjecture, Combinatorics, Twin prime, Prime number, Number theory

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