An anticlique in N is a set of integers containing no pair of elements such that one is a multiple of the other. For every positive integer we give a necessary and sufficient condition on n for the set {1, 2, ..., } to admit an anticlique of cardinality containing

There is a probability charge on the power set of the integers that gives probability 1/p to every residue class modulo a prime p. There exists such a charge that gives probability w to the set of prime numbers iff w ∈ [0, 1/2]. Similarly, there is such a charge that gives probability x to the...

We are going to discuss enormous integers and rates of growth after [PH77]. This breakthrough was based on a variant of the classical finite Ramsey theorem. Since then, examples have been given of greater relevance to a number of standard mathematical and computer science contexts, often...

This note presents a pair of specialized integers factorization algorithms. The first algorithm can factor odd composite integers into two nearly equal factors, assuming their existence, and the second algorithm can factor a large class of composite integers = that meet certain criterion