Small Mersenne Prime Factors (page 937/5025)

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
8714963	17429927	8	~1985
8715023	17430047	8	~1985
8715383	17430767	8	~1985
8715659	17431319	8	~1985
8716007	226616183	9	~1988
8716021	348640841	9	~1988
8716063	139457009	9	~1987
8716217	1255135249	10	~1990
8716271	17432543	8	~1985
8716439	17432879	8	~1985
8716627	87166271	8	~1987
8716703	17433407	8	~1985
8716997	52301983	8	~1986
8717117	52302703	8	~1986
8717123	17434247	8	~1985
8717557	1394809121	10	~1990
8717783	17435567	8	~1985
8717963	17435927	8	~1985
8717981	52307887	8	~1986
8718089	1952851937	10	~1990
8718191	17436383	8	~1985
8718401	52310407	8	~1986
8718427	209242249	9	~1988
8718431	17436863	8	~1985
8718491	17436983	8	~1985

Exp.	Prime Factor	Digits	Year
8718539	69748313	8	~1987
8718733	52312399	8	~1986
8718737	52312423	8	~1986
8718811	87188111	8	~1987
8719127	69753017	8	~1987
8719133	52314799	8	~1986
8719211	17438423	8	~1985
8719253	52315519	8	~1986
8719303	209263273	9	~1988
8719391	17438783	8	~1985
8719831	156956959	9	~1988
8719873	558071873	9	~1989
8720171	17440343	8	~1985
8720311	87203111	8	~1987
8720483	17440967	8	~1985
8720533	52323199	8	~1986
8721029	69768233	8	~1987
8721101	331401839	9	~1988
8721239	17442479	8	~1985
8721239	69769913	8
8721607	348864281	9	~1988
8721749	1378036343	10	~1990
8721763	139548209	9	~1987
8721913	52331479	8	~1986
8722097	52332583	8	~1986

Exp.	Prime Factor	Digits	Year
8722409	69779273	8	~1987
8722607	69780857	8	~1987
8722799	17445599	8	~1985
8723063	17446127	8	~1985
8723213	52339279	8	~1986
8723321	69786569	8	~1987
8723441	52340647	8	~1986
8723459	69787673	8	~1987
8723531	17447063	8	~1985
8723789	69790313	8	~1987
8723993	52343959	8	~1986
8724143	17448287	8	~1985
8724641	52347847	8	~1986
8724721	52348327	8	~1986
8725091	17450183	8	~1985
8725177	52351063	8	~1986
8725217	52351303	8	~1986
8725421	69803369	8	~1987
8725511	17451023	8	~1985
8725621	261768631	9	~1988
8725631	17451263	8	~1985
8725823	17451647	8	~1985
8726351	17452703	8	~1985
8727053	52362319	8	~1986
8727161	69817289	8	~1987

Exp.	Prime Factor	Digits	Year
8727263	17454527	8	~1985
8727343	139637489	9	~1987
8728303	296762303	9	~1988
8728427	157111687	9	~1988
8728679	17457359	8	~1985
8728757	52372543	8	~1986
8728823	17457647	8	~1985
8728969	192037319	9	~1988
8729183	17458367	8	~1985
8729291	17458583	8	~1985
8729317	52375903	8	~1986
8729411	17458823	8	~1985
8729543	17459087	8	~1985
8729711	69837689	8	~1987
8729821	52378927	8	~1986
8730083	17460167	8	~1985
8730331	139685297	9	~1987
8730983	17461967	8	~1985
8731031	17462063	8	~1985
8731531	87315311	8	~1987
8731939	87319391	8	~1987
8732051	17464103	8	~1985
8732093	52392559	8	~1986
8732201	52393207	8	~1986
8732261	52393567	8	~1986

4.724.182 digits

25-04-13