Conjectures On Primes And Fermat Pseudoprimes Many Based On Smarandache Function
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Conjectures on Primes and Fermat Pseudoprimes, Many Based on Smarandache Function
It is always difficult to talk about arithmetic, because those who do not know what is about, nor do they understand in few sentences, no matter how inspired these might be, and those who know what is about, do no need to be told what is about. Arithmetic is that branch of mathematics that you keep it in your soul and in your mind, not in your suitcase or laptop. Part One of this book of collected papers aims to show new applications of Smarandache function in the study of some well known classes of numbers, like Sophie Germain primes, Poulet numbers, Carmichael numbers ets. Beside the well-known notions of number theory, we defined in these papers the following new concepts: “Smarandache-Coman divisors of order k of a composite integer n with m prime factors”, “Smarandache-Coman congruence on primes”, “Smarandache-Germain primes”, Coman-Smarandache criterion for primality”, “Smarandache-Korselt criterion”, “Smarandache-Coman constants”. Part Two of this book brings together several papers on few well known and less known types of primes.
TWO HUNDRED AND THIRTEEN CONJECTURES ON PRIMES
In two of my previous published books, “Two hundred conjectures and one hundred and fifty open problems on Fermat pseudoprimes”, respectively “Conjectures on primes and Fermat pseudoprimes, many based on Smarandache function”, I already expressed my passion for integer numbers, especially for primes and Fermat pseudoprimes, fascinating numbers that seem to be a little bit more willing to let themselves ordered and understood than the prime numbers.
SEQUENCES OF INTEGERS, CONJECTURES AND NEW ARITHMETICAL TOOLS (COLLECTED PAPERS)
Part One of this book of collected papers brings together papers regarding conjectures on primes, twin primes, squares of primes, semiprimes, different types of pairs of primes, recurrent sequences, other sequences of integers related to primes created through concatenation and in other ways. Part Two brings together several articles presenting the notions of c-primes, m-primes, c-composites and m-composites (c/m integers), also the notions of g-primes, s-primes, g-composites and s-composites (g/s integers) and show some of the applications of these notions. Part Three presents the notions of “Mar constants” and “Smarandache-Coman constants”, useful to highlight the periodicity of some infinite sequences of positive integers (sequences of squares, cubes, triangualar numbers) , respectively in the analysis of Smarandache concatenated sequences. Part Four presents the notion of Smarandache-Coman sequences, id est the sequences of primes formed through different arithmetical operations on the terms of Smarandache concatenated sequences. Part Five presents the notion of Smarandache-Coman function, a function based on the Smarandache function which seems to be particularly interesting: beside other notable characteristics, it seems to have as values all the prime numbers and, more than that, they seem to appear, leaving aside the non-prime values, in natural order. This book of collected papers seeks to expand the knowledge on some well known classes of numbers and also to define new classes of primes or classes of integers directly related to primes.