Authors: Marius Coman
Though the well known Fermat’s conjecture on the diophantine equation x^n + y^n = z^n is named “Fermat’s big theorem”, in fact probably much more important for number theory is what is called “Fermat’s little theorem” which was the most important step up to that time in order to discover a primality criterion. This exceptional criterion of primality still has its exceptions: Fermat pseudoprimes, numbers which “behave” like primes though they are no primes; but they are still a class of numbers at least as interesting as the class of primes. Among Fermat pseudoprimes two classes of numbers are particularly distinguished: Poulet numbers (relative Fermat pseudoprimes) and Carmichael numbers (absolute Fermat pseudoprimes). The initial aim of this paper was only to see which Poulet numbers can be obtained concatenating primes (or, in other words, whichever admit a deconcatenation in prime numbers) but, inspired by a characteristic of a subset of Poulet numbers, I also made the following conjecture: there exist an infinity of primes p obtained concatenating to the right a prime q having the sum of the digits s(q) equal to a multiple of 5 with 3.
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[v1] 2016-03-21 03:18:13
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