In three of my previous published books, namely “Two hundred conjectures and one hundred and fifty open problems on Fermat pseudoprimes”, “Conjectures on primes and Fermat pseudoprimes, many based on Smarandache function” and “Two hundred and thirteen conjectures on primes”, I showed my passion for conjectures on sequences of integers. In spite the fact that some mathematicians stubbornly understand mathematics as being just the science of solving and proving, my books of conjectures have been well received by many enthusiasts of elementary number theory, which gave me confidence to continue in this direction. Part One of this book brings together papers regarding conjectures on primes, twin primes, squares of primes, semiprimes, different types of pairs or triplets of primes, recurrent sequences, sequences of integers created through concatenation and other sequences of integers related to primes. Part Two of this book brings together several articles which present 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 (because this is not a book structured unitary from the beginning but a book of collected papers, I defined the notions mentioned in various papers, but the best definition of them can be found in Addenda to the paper numbered tweny-nine), in the study of the squares of primes, Fermat pseudoprimes and generally in Diophantine analysis. Part Three of this book presents the notions of “Coman constants” and “Smarandache-Coman constants”, useful to highlight the periodicity of some infinite sequences of positive integers (sequences of squares, cubes, triangular numbers, polygonal numbers), respectively in the analysis of Smarandache concatenated sequences. Part Four of this book presents the notion of Smarandache-Coman sequences, id est sequences of primes formed through different arithmetical operations on the terms of Smarandache concatenated sequences. Part Five of this book presents the notion of Smarandache-Coman function, a function based on the well known Smarandache function which seems to be particularly interesting: beside other 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.