This book brings together fifty-two papers regarding primes and Fermat pseudoprimes, submitted by the author to the scientific database Research Gate. Part One of this book, “Sequences of primes and conjectures on them”, contains papers on sequences of primes, squares of primes, semiprimes, pairs, triplets and quadruplets of primes and conjectures on them. This part also contains papers on possible methods to obtain large primes, some of them based on concatenation, some of them on other arithmetical operations. It is also introduced a new notion, “Smarandache-Coman sequences of primes”, defined as “all sequences of primes obtained from the Smarandache sequences using any arithmetical operation”. Part Two of this book, “Sequences of Fermat pseudoprimes and conjecture on them”, contains sequences of Poulet and Carmichael numbers. Among these papers there is a list of thirty-six polynomials and formulas that generate sequences of Fermat pseudoprimes. Part Three of this book, “Prime producing quadratic polynomials”, contains three papers which list few already known such polynomials, that generate more than 20, 30 or even 40 primes in a row, and few such polynomials discoverd by the author himself (in a review of records in the field of prime generating polynomials, written by Dress and Landreau, two mathematicians well known for their contributions in this field, the author is mentioned with 18 prime producing quadratic polynomials). One of these three papers proposes 17 generic formulas that may generate prime producing quadratic polynomials.