A History of the Sieve Process

Publisher Summary This chapter presents the history of the sieve process. In a sieve problem, two numbers are given A and B, k integers or moduli, k other integers, and a matrix, and the problem is to find an unknown integer x that satisfies an equation. The sieve problem is to find all those integers satisfying the two kinds of conditions, congruential conditions, and inequalities. The chapter discusses that there is another type of sieve problem called quadratic in which n i is approximately equal to ½ m i . This means that a random X has about a 50% chance of satisfying any one of these congruences and if one has k of these the number X has about one chance in 2 k . The sieve method had a relay, some contacts, and circuitry that was very primitive but quite effective. The sieve has the advantage over the stencil method in that one do not have to plan in advance how one wish to go and apply carefully one stencil after another. It was a genuine parallel machine.