Small Mersenne Prime Factors (page 484/5745)

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
2733361	568539089	9	~1986
2733427	27334271	8	~1983
2733589	60138959	8	~1984
2733823	27338231	8	~1983
2733851	21870809	8	~1983
2733971	21871769	8	~1983
2734117	43745873	8	~1983
2734141	43746257	8	~1983
2734219	27342191	8	~1983
2734283	71091359	8	~1984
2734481	21875849	8	~1983
2734573	16407439	8	~1982
2734643	5469287	7	~1981
2734717	16408303	8	~1982
2734793	16408759	8	~1982
2735009	21880073	8	~1983
2735017	43760273	8	~1983
2735017	262561633	9
2735339	5470679	7	~1981
2735581	848030111	9	~1987
2735699	21885593	8	~1983
2735983	27359831	8	~1983
2735983	65663593	8
2736229	65669497	8	~1984
2736263	5472527	7	~1981

Exp.	Prime Factor	Digits	Year
2736491	5472983	7	~1981
2736497	38310959	8	~1983
2736523	27365231	8	~1983
2736533	16419199	8	~1982
2736533	38311463	8
2736623	71152199	8	~1984
2736733	16420399	8	~1982
2736911	71159687	8	~1984
2737043	5474087	7	~1981
2737057	43792913	8	~1983
2737081	60215783	8	~1984
2737093	16422559	8	~1982
2737109	104010143	9	~1984
2737211	71167487	8	~1984
2737213	16423279	8	~1982
2737523	5475047	7	~1981
2737649	21901193	8	~1983
2737661	16425967	8	~1982
2737723	114984367	9	~1985
2737873	372350729	9	~1986
2737997	38331959	8	~1983
2738051	5476103	7	~1981
2738063	5476127	7	~1981
2738117	481908593	9	~1986
2738381	16430287	8	~1982

Exp.	Prime Factor	Digits	Year
2738423	5476847	7	~1981
2738579	5477159	7	~1981
2738639	5477279	7	~1981
2738707	27387071	8	~1983
2738761	16432567	8	~1982
2739013	82170391	8	~1984
2739043	27390431	8	~1983
2739133	43826129	8	~1983
2739281	87656993	8	~1984
2739419	5478839	7	~1981
2739437	21915497	8	~1983
2739637	16437823	8	~1982
2739701	16438207	8	~1982
2739773	38356823	8	~1983
2740211	21921689	8	~1983
2740319	5480639	7	~1981
2740393	16442359	8	~1982
2740453	16442719	8	~1982
2740511	5481023	7	~1981
2740559	21924473	8	~1983
2740559	49330063	8
2740607	49330927	8	~1984
2740631	71256407	8	~1984
2740817	3245127329	10	~1988
2740853	16445119	8	~1982

Exp.	Prime Factor	Digits	Year
2740867	27408671	8	~1983
2740999	115121959	9	~1985
2741009	169942559	9	~1985
2741147	21929177	8	~1983
2741231	21929849	8	~1983
2741231	460526809	9
2741351	5482703	7	~1981
2741357	38378999	8	~1983
2741357	65792569	8
2741489	38380847	8	~1983
2741513	197388937	9	~1985
2741617	16449703	8	~1982
2741621	21932969	8	~1983
2741653	60316367	8	~1984
2741741	21933929	8	~1983
2741779	27417791	8	~1983
2741867	21934937	8	~1983
2741939	5483879	7	~1981
2741993	235811399	9	~1985
2742031	27420311	8	~1983
2742163	27421631	8	~1983
2742199	27421991	8	~1983
2742241	16453447	8	~1982
2742241	43875857	8
2742241	60329303	8

5.441.361 digits

26-03-15