Authors: Marius Coman
The definition of “concatenation” in mathematics is, according to Wikipedia, “the joining of two numbers by their numerals. That is, the concatenation of 69 and 420 is 69420”. Though the method of concatenation is widely considered as a part of so called “recreational mathematics”, in fact this method can often lead to very “serious” results, and even more than that, to really amazing results. This is the purpose of this book: to show that this method, unfairly neglected, can be a powerful tool in number theory. In particular, as revealed by the title, I used the method of concatenation in this book to obtain possible infinite sequences of primes. Part One of this book, “Primes in Smarandache concatenated sequences and Smarandache-Coman sequences”, contains 12 papers on various sequences of primes that are distinguished among the terms of the well known Smarandache concatenated sequences (S sequences) but also on “Smarandache-Coman sequences of primes” (SC sequences), defined by the author as “all sequences of primes obtained from the terms of Smarandache sequences using any arithmetical operation”: the SC sequences presented in this book are related, of course, to concatenation, but in three different ways: the S sequence is obtained by the method of concatenation but the operation applied on its terms is some other arithmetical operation; the S sequence is not obtained by the method of concatenation but the operation applied on its terms is concatenation, or both S sequence and SC sequence are using the method of concatenation. Part Two of this book, “Sequences of primes obtained by the method of concatenation”, brings together 51 articles which aim, using the mentioned method, to highlight sequences of numbers that are rich in primes or are liable to lead to large primes. The method of concatenation is applied to different classes of numbers, e.g. squares of primes, Poulet numbers, triangular numbers, reversible primes, twin primes, repdigits, factorials, primorials, in order to obtain sequences, possible infinite, of primes. Part Two of this book also contains a paper which lists a number of 33 sequences of primes obtained by the method of concatenation, sequences presented and analyzed in more detail in my previous papers, gathered together in five books of collected papers: “Two hundred conjectures and one hundred and fifty open problems on Fermat pseudoprimes”, “Two hundred and thirteen conjectures on primes”, “Conjectures on primes and Fermat pseudoprimes, many based on Smarandache function”, “Sequences of integers, conjectures and new arithmetical tools”, “Formulas and polynomials which generate primes and Fermat pseudoprimes”.
Comments: 150 Pages. Published by Education Publishing, USA. Copyright 2016 by Marius Coman.
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