Parallel Computers, Number Theory Problems, and Experimental Results

This paper discusses the number theoretic problems of primality testing and factorization. It presents algorithms for these problems. and reports on six implementations. Original work is presented for three machines (DADO [Stolfo 83], the Intel Hypercube [Hypercube 86] and the Sequent Balance [Balance 86]). DADO runs primality testing and trial-divisors factorization. The Balance and Hypercube execute factorization by elliptic curves [Lenstra 86]. Work by other researchers is due to [Batcher 86, Pomerance 86, Silverman 86 and Wunderlich]; these implementations use a network of workstations, a special-purpose parallel sieve machine and the Massively Parallel Processor (MPP). The 16K1processor memory of the current DADO2 machine was too small to execute the elliptic curve program, though it was ample for trial-divisors factorization