Small Mersenne Prime Factors (page 769/5610)

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
5834243	11668487	8	~1984
5834291	11668583	8	~1984
5834351	11668703	8	~1984
5834377	35006263	8	~1985
5834431	93350897	8	~1986
5834579	11669159	8	~1984
5834593	35007559	8	~1985
5834831	11669663	8	~1984
5835043	245071807	9	~1987
5835059	11670119	8	~1984
5835209	46681673	8	~1985
5835341	46682729	8	~1985
5835343	58353431	8	~1986
5835497	315116839	9	~1987
5835581	35013487	8	~1985
5835601	35013607	8	~1985
5835971	11671943	8	~1984
5836079	11672159	8	~1984
5836087	58360871	8	~1986
5836451	46691609	8	~1985
5836459	58364591	8	~1986
5836751	46694009	8	~1985
5836771	58367711	8	~1986
5836807	105062527	9	~1986
5836823	326862089	9	~1987

Exp.	Prime Factor	Digits	Year
5837053	35022319	8	~1985
5837399	11674799	8	~1984
5837501	175125031	9	~1987
5837543	11675087	8	~1984
5837597	35025583	8	~1985
5837603	11675207	8	~1984
5837627	140103049	9	~1986
5837633	35025799	8	~1985
5837719	58377191	8	~1986
5837831	11675663	8	~1984
5837879	11675759	8	~1984
5837939	46703513	8	~1985
5837999	186815969	9	~1987
5838017	46704137	8	~1985
5838071	11676143	8	~1984
5838211	93411377	8	~1986
5838221	35029327	8	~1985
5838331	93413297	8	~1986
5838383	11676767	8	~1984
5838449	81738287	8	~1986
5838593	35031559	8	~1985
5838641	35031847	8	~1985
5838659	11677319	8	~1984
5838713	35032279	8	~1985
5838887	46711097	8	~1985

Exp.	Prime Factor	Digits	Year
5838929	46711433	8	~1985
5838971	11677943	8	~1984
5838991	58389911	8	~1986
5839567	140149609	9	~1986
5839573	35037439	8	~1985
5839577	46716617	8	~1985
5839649	46717193	8	~1985
5839657	35037943	8	~1985
5839979	11679959	8	~1984
5840077	35040463	8	~1985
5840077	280323697	9
5840113	35040679	8	~1985
5840293	35041759	8	~1985
5840579	46724633	8	~1985
5840699	11681399	8	~1984
5840699	46725593	8
5840761	35044567	8	~1985
5840969	140183257	9	~1986
5841239	11682479	8	~1984
5841323	11682647	8	~1984
5841443	11682887	8	~1984
5841601	35049607	8	~1985
5841991	93471857	8	~1986
5842283	11684567	8	~1984
5842399	58423991	8	~1986

Exp.	Prime Factor	Digits	Year
5842691	11685383	8	~1984
5842703	11685407	8	~1984
5842703	151910279	9
5842841	35057047	8	~1985
5842871	11685743	8	~1984
5842877	46743017	8	~1985
5843603	151933679	9	~1987
5843653	35061919	8	~1985
5843707	280497937	9	~1987
5843837	35063023	8	~1985
5843951	11687903	8	~1984
5843953	35063719	8	~1985
5844203	11688407	8	~1984
5844329	46754633	8	~1985
5844361	35066167	8	~1985
5844539	11689079	8	~1984
5844679	105204223	9	~1986
5844733	93515729	8	~1986
5844851	11689703	8	~1984
5845039	58450391	8	~1986
5845523	11691047	8	~1984
5845589	315661807	9	~1987
5845781	35074687	8	~1985
5845793	35074759	8	~1985
5845871	46766969	8	~1985

5.307.017 digits

26-01-11