Number Theory

    

Conjecture on the Consecutive Concatenation of the Terms of an Arithmetic Progression

Authors: Marius Coman

In this paper I make the following conjecture: for any arithmetic progression a + b*k, where at least one of a and b is different than 1, that also satisfies the conditions imposed by the Dirichlet’s Theorem (a and b are positive coprime integers) is true that the sequence obtained by the consecutive concatenation of the terms a + b*k has an infinity of prime terms. Example: for [a, b] = [7, 11], the sequence obtained by consecutive concatenation of 7, 18, 29, 40, 51, 62, 73 (...) has the prime terms 718294051, 7182940516273 (...). If this conjecture were true, the fact that the Smarandache consecutive numbers sequence 1, 12, 123, 1234, 12345 (...) could have not any prime term (thus far there is no prime number known in this sequence, though there have been checked the first about 40 thousand terms) would be even more amazing.

Comments: 4 Pages.

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Submission history

[v1] 2016-04-03 14:07:45

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