Small Mersenne Prime Factors (page 737/5610)

Small Mersenne Prime Factors
Prime numbers of the form M_p= 2^p − 1 are called Mersenne primes. For M_p to be prime, p must also be prime.
Any factor q of a Mersenne number 2^p − 1 must be of the form 2kp + 1, where integer k ≥ 0. Furthermore, q must be 1 or 7 mod 8.

Exp.	Prime Factor	Digits	Year
5427431	10854863	8	~1984
5427473	32564839	8	~1985
5427671	10855343	8	~1984
5427809	75989327	8	~1986
5427899	10855799	8	~1984
5427923	10855847	8	~1984
5428387	54283871	8	~1985
5428561	32571367	8	~1985
5428571	43428569	8	~1985
5428673	76001423	8	~1986
5428679	10857359	8	~1984
5428783	217151321	9	~1987
5429071	54290711	8	~1985
5429107	488619631	9	~1988
5429147	130299529	9	~1986
5429321	43434569	8	~1985
5429401	32576407	8	~1985
5429731	54297311	8	~1985
5429807	43438457	8	~1985
5430059	10860119	8	~1984
5430317	43442537	8	~1985
5430349	130328377	9	~1986
5430443	10860887	8	~1984
5430791	10861583	8	~1984
5430907	54309071	8	~1985

Exp.	Prime Factor	Digits	Year
5430959	10861919	8	~1984
5430961	32585767	8	~1985
5431037	32586223	8	~1985
5431121	43448969	8	~1985
5431277	32587663	8	~1985
5431799	10863599	8	~1984
5431819	54318191	8	~1985
5431949	43455593	8	~1985
5432087	43456697	8	~1985
5432351	10864703	8	~1984
5432351	97782319	8
5432417	43459337	8	~1985
5432579	43460633	8	~1985
5432597	76056359	8	~1986
5432621	32595727	8	~1985
5433101	32598607	8	~1985
5433293	32599759	8	~1985
5433343	54333431	8	~1985
5433419	10866839	8	~1984
5433431	43467449	8	~1985
5433479	10866959	8	~1984
5433517	32601103	8	~1985
5433731	10867463	8	~1984
5433731	97807159	8
5433787	86940593	8	~1986

Exp.	Prime Factor	Digits	Year
5433839	10867679	8	~1984
5433997	32603983	8	~1985
5434031	43472249	8	~1985
5434349	163030471	9	~1986
5434409	173901089	9	~1987
5434661	43477289	8	~1985
5434697	32608183	8	~1985
5434937	32609623	8	~1985
5434997	163049911	9	~1986
5435399	10870799	8	~1984
5435519	10871039	8	~1984
5435723	10871447	8	~1984
5435959	228310279	9	~1987
5436113	32616679	8	~1985
5436217	32617303	8	~1985
5436577	32619463	8	~1985
5436653	76113143	8	~1986
5436803	141356879	9	~1986
5436881	32621287	8	~1985
5437169	43497353	8	~1985
5437273	32623639	8	~1985
5437343	10874687	8	~1984
5437373	32624239	8	~1985
5437403	10874807	8	~1984
5437507	54375071	8	~1985

Exp.	Prime Factor	Digits	Year
5437643	10875287	8	~1984
5437979	10875959	8	~1984
5438099	10876199	8	~1984
5438099	43504793	8
5438131	217525241	9	~1987
5438183	10876367	8	~1984
5438273	76135823	8	~1986
5438359	54383591	8	~1985
5438483	10876967	8	~1984
5438639	43509113	8	~1985
5438651	10877303	8	~1984
5438663	10877327	8	~1984
5439191	10878383	8	~1984
5439227	43513817	8	~1985
5439299	10878599	8	~1984
5439299	271964951	9
5439341	43514729	8	~1985
5439361	87029777	8	~1986
5439697	32638183	8	~1985
5439727	54397271	8	~1985
5439743	10879487	8	~1984
5440007	1305601681	10	~1989
5440217	32641303	8	~1985
5440223	10880447	8	~1984
5440343	10880687	8	~1984

5.307.017 digits

26-01-11