Reports the factor-filtering and primality-testing of Mersenne Numbers Mp for p < 100000, the latter using the ICL 'DAP' Distributed Array Processor

Haworth, Guy McCrossan

English

Central Archive at the University of Reading

Abstracts of the American Mathematical Society, Vol. 7, No. 2, pp. 224-225. ISSN 0192-5857:    *86T-11-857  G McC HAWORTH: 33, Alexandra Rd., Reading, Berks UK, RG1 5PG.              Primality-testing Mersenne Numbers (II). Preliminary Report. Mp = 2p-1, index p prime, is a Mersenne Number.  Let S1 = 4 and let Sn+1 = Sn2-2 mod Mp.  The Mp Lucas-Lehmer primality test (Mp-LLT) is "Mp prime ⇔ residue Sp-1 = 0" for p > 2. Codes A and B exercised Mp-LLT [AMS Abstracts, v4 no2 (Feb '83) p196, 83T-10-82] over the p < 62982 range, including all Mp for which no factor was known.  By November '84, Code C had extended the coverage, testing the 1362 Mp for which no factor was known in the range 62982 < p < 100000.  The three codes run on the ICL DAP at QMC London and use Fast Fermat-number-transform multiplication. Code C tested 16 Mp in parallel and checked the squaring modulo 216-1 without signalling any faults.  It confirmed M86243 prime in effectively 2318 seconds and also confirmed 520 other known Mp-LRs. The consolidated and filed results comprise:      a) M50021-f1, M50023-f1 and 2620 Mp-f1 for 50024 < p < 100000      b) the previous 2828 second-sourced Mp-LRs for p < 50024      c) 1837 single-sourced Mp-LRs for 50024 < p < 100000      d) references to Mp-f1 tables for p < 50000 and to known Mp-LR sources. The author gratefully acknowledges the computing provided by the National DAP Service at Queen Mary College and the assistance of Grant Bowgen and Steve Davies who produced the final computations. (Received November 8, 1985) (Sponsored by Samuel S. Wagstaff, Jr.) 

Primality-testing Mersenne Numbers (II)

Abstract

Similar works

Full text

Available Versions

Central Archive at the University of Reading