Part One of this book, “Sequences of primes and conjectures on them”, brings together thirty-two papers regarding sequences of primes, sequences of squares of primes, sequences of certain types of semiprimes, also few types of pairs, triplets and quadruplets of primes and conjectures on all of these sequences. There are also few papers regarding possible methods to obtain large primes or very large numbers with very few prime factors, some of them based on concatenation, some of them on other arithmetic operations. It is also introduced a new notion: “Smarandache-Coman sequences of primes”, defined as “all sequences of primes obtained from the terms of Smarandache sequences using any arithmetical operation” (for instance, the sequence of primes obtained concatenating to the right with the digit one the terms of Smarandache consecutive numbers sequence). Part Two of this book, “Sequences of Fermat pseudoprimes and conjectures on them”, brings together seventeen papers on sequences of Poulet numbers and Carmichael numbers, i.e. the Fermat pseudoprimes to base 2 and the absolute Fermat pseudoprimes, two classes of numbers that fascinated the author for long time. 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 some already known such polynomials, that generate more than 20, 30 or even 40 primes in a row, and few such polynomials discovered by the author himself (in a review of records in the field of prime generating polynomials, written by Dress and Landreau, two French mathematicians well known for records in this field, review that can be found on the web adress , the author – he says this proudly, of course – is mentioned with 18 prime producing quadratic polynomials). One of the papers proposes seventeen generic formulas that may generate prime-producing quadratic polynomials.

The purpose of this book is to show that the method of concatenation can be a powerful tool in number theory and, in particular, in obtaining possible infinite sequences of primes. Part One of this book, “Primes in Smarandache concatenated sequences and Smarandache-Coman sequences of primes” , contains 12 papers on various sequences of primes that are distinguished among the terms of the well known Smarandache concatenated sequences. The sequences presented in this part are related to concatenation in three different ways: the sequence is obtained by the method of concatenation but the operation applied on its terms is some other arithmetical operation; the sequence is not obtained by concatenation but the operation applied on its terms is concatenation or both the sequence and the operation applied on its terms (in order to find sequences of primes) 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 which 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. Poulet numbers, twin primes, reversible primes, triangular numbers, repdigits, factorial numbers, fibonorial numbers, primordial numbers in order to obtain sequences of primes.

This book explores the interplay between the two main currents of mathematics, the continuous and the discrete.

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium senes. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book of Records, reminded me very gently that the most "innumerate" people of the world are of a certain trible in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes, Morris, I'm from Brazil, but my book will contain numbers different from ·one.''' He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name) and consists of about 16 million decimal digits of the number Te. "I assure you, Morris, that in spite of the beauty of the appar ent randomness of the decimal digits of Te, I'll be sure that my text will include also some words." And then I proceeded putting together the magic combina tion of words and numbers, which became The Book of Prime Number Records. If you have seen it, only extreme curiosity could impel you to have this one in your hands. The New Book of Prime Number Records differs little from its predecessor in the general planning. But it contains new sections and updated records.

Bridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Authors are well-known and highly-regarded in the field