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2016•viXraOpen access

Primes obtained concatenating n consecutive numbers and then the resulting number with 1

Marius Coman

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Abstract

In this paper I state the following conjecture: For any positive integer n, n > 1, there exist a sequence having an infinity of prime terms obtained concatenating n consecutive numbers and then the resulting number, to the right, with 1. Examples: for n = 2, the sequence obtained this way contains the primes 10111, 15161, 18191, 21221 (...); for n = 9, the sequence obtained this way contains the primes 1234567891, 910111213141516171, 2021222324252627281, 2930313233343536371 (...).

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What this paper is about

In this paper I state the following conjecture: For any positive integer n, n > 1, there exist a sequence having an infinity of prime terms obtained concatenating n consecutive numbers and then the resulting number, to the right, with 1. Examples: for n = 2, the sequence obtained this way contains the primes 10111, 15161, 18191, 21221 (...); for n = 9, the sequence obtained this way contains the primes 1234567891, 910111213141516171, 2021222324252627281, 2930313233343536371 (...).

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Available abstract

In this paper I state the following conjecture: For any positive integer n, n > 1, there exist a sequence having an infinity of prime terms obtained concatenating n consecutive numbers and then the resulting number, to the right, with 1. Examples: for n = 2, the sequence obtained this way contains the primes 10111, 15161, 18191, 21221 (...); for n = 9, the sequence obtained this way contains the primes 1234567891, 910111213141516171, 2021222324252627281, 2930313233343536371 (...).

Key concepts: Sequence (biology), Infinity, Combinatorics, Conjecture, Number theory, Mathematics, Prime number, Integer (computer science)

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