Small Mersenne Prime Factors (page 767/5610)

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
5806961	34841767	8	~1985
5807159	11614319	8	~1984
5807533	34845199	8	~1985
5807579	11615159	8	~1984
5807579	46460633	8
5807701	92923217	8	~1986
5807831	11615663	8	~1984
5808059	11616119	8	~1984
5808083	11616167	8	~1984
5808157	139395769	9	~1986
5808227	46465817	8	~1985
5808287	46466297	8	~1985
5808697	34852183	8	~1985
5808701	46469609	8	~1985
5808899	11617799	8	~1984
5808989	46471913	8	~1985
5809093	34854559	8	~1985
5809103	11618207	8	~1984
5809109	46472873	8	~1985
5809123	92945969	8	~1986
5809151	11618303	8	~1984
5809283	11618567	8	~1984
5809403	11618807	8	~1984
5809451	11618903	8	~1984
5809613	34857679	8	~1985

Exp.	Prime Factor	Digits	Year
5809883	11619767	8	~1984
5810201	46481609	8	~1985
5810279	11620559	8	~1984
5810407	92966513	8	~1986
5810699	11621399	8	~1984
5810771	11621543	8	~1984
5811419	11622839	8	~1984
5811419	46491353	8
5811521	174345631	9	~1987
5811527	46492217	8	~1985
5811529	127853639	9	~1986
5811727	278962897	9	~1987
5811731	11623463	8	~1984
5811959	11623919	8	~1984
5812259	11624519	8	~1984
5812343	11624687	8	~1984
5812361	174370831	9	~1987
5812397	46499177	8	~1985
5812403	11624807	8	~1984
5812463	11624927	8	~1984
5812661	46501289	8	~1985
5812931	11625863	8	~1984
5812957	34877743	8	~1985
5812991	11625983	8	~1984
5813051	186017633	9	~1987

Exp.	Prime Factor	Digits	Year
5813347	104640247	9	~1986
5813441	34880647	8	~1985
5813527	232541081	9	~1987
5813579	11627159	8	~1984
5814091	232563641	9	~1987
5814317	81400439	8	~1986
5814407	46515257	8	~1985
5814467	46515737	8	~1985
5814839	11629679	8	~1984
5814857	34889143	8	~1985
5814983	11629967	8	~1984
5815151	11630303	8	~1984
5815163	11630327	8	~1984
5815211	46521689	8	~1985
5815331	46522649	8	~1985
5815721	46525769	8	~1985
5815811	11631623	8	~1984
5816243	11632487	8	~1984
5816339	11632679	8	~1984
5816387	46531097	8	~1985
5816453	34898719	8	~1985
5816549	46532393	8	~1985
5816611	232664441	9	~1987
5816971	58169711	8	~1986
5817061	34902367	8	~1985

Exp.	Prime Factor	Digits	Year
5817061	127975343	9
5817347	46538777	8	~1985
5817541	511943609	9	~1988
5817653	34905919	8	~1985
5817907	58179071	8	~1986
5818073	34908439	8	~1985
5818277	34909663	8	~1985
5818283	11636567	8	~1984
5818391	11636783	8	~1984
5818493	34910959	8	~1985
5818619	11637239	8	~1984
5818819	58188191	8	~1986
5818853	558609889	9	~1988
5819189	314236207	9	~1987
5819279	11638559	8	~1984
5819293	34915759	8	~1985
5819543	11639087	8	~1984
5819557	34917343	8	~1985
5819647	232785881	9	~1987
5819773	93116369	8	~1986
5820041	46560329	8	~1985
5820233	34921399	8	~1985
5820421	34922527	8	~1985
5820481	34922887	8	~1985
5820583	58205831	8	~1986

5.307.017 digits

26-01-11