Small Mersenne Prime Factors (page 761/5985)

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
5538359	99690463	8	~1986
5538361	33230167	8	~1985
5538691	88619057	8	~1986
5538857	33233143	8	~1985
5538893	33233359	8	~1985
5538943	55389431	8	~1985
5538947	44311577	8	~1985
5539199	11078399	8	~1984
5539211	11078423	8	~1984
5539309	221572361	9	~1987
5539403	11078807	8	~1984
5539477	221579081	9	~1987
5539601	44316809	8	~1985
5540141	33240847	8	~1985
5540177	33241063	8	~1985
5540287	55402871	8	~1985
5540393	33242359	8	~1985
5540471	11080943	8	~1984
5540659	55406591	8	~1985
5540939	11081879	8	~1984
5541037	33246223	8	~1985
5541251	11082503	8	~1984
5541583	55415831	8	~1985
5541611	11083223	8	~1984
5541857	33251143	8	~1985

Exp.	Prime Factor	Digits	Year
5542013	133008313	9	~1986
5542127	277106351	9	~1987
5542259	11084519	8	~1984
5542673	33256039	8	~1985
5542703	11085407	8	~1984
5542753	33256519	8	~1985
5542777	1585234223	10	~1989
5543297	33259783	8	~1985
5543399	11086799	8	~1984
5543507	99783127	8	~1986
5543831	11087663	8	~1984
5543873	77614223	8	~1986
5543981	44351849	8	~1985
5544509	44356073	8	~1985
5544659	11089319	8	~1984
5544683	11089367	8	~1984
5544689	44357513	8	~1985
5544743	11089487	8	~1984
5544779	44358233	8	~1985
5544821	33268927	8	~1985
5544911	11089823	8	~1984
5544971	11089943	8	~1984
5545481	33272887	8	~1985
5545499	11090999	8	~1984
5545567	55455671	8	~1985

Exp.	Prime Factor	Digits	Year
5545649	44365193	8	~1985
5545697	33274183	8	~1985
5545751	11091503	8	~1984
5545871	44366969	8	~1985
5545913	166377391	9	~1987
5546393	33278359	8	~1985
5546479	133115497	9	~1986
5546483	11092967	8	~1984
5546543	11093087	8	~1984
5546753	33280519	8	~1985
5546771	11093543	8	~1984
5546903	11093807	8	~1984
5547011	11094023	8	~1984
5547247	55472471	8	~1985
5547277	88756433	8	~1986
5547317	77662439	8	~1986
5547371	44378969	8	~1985
5547467	44379737	8	~1985
5547499	221899961	9	~1987
5547599	11095199	8	~1984
5547733	33286399	8	~1985
5547779	11095559	8	~1984
5547863	11095727	8	~1984
5547911	11095823	8	~1984
5547959	11095919	8	~1984

Exp.	Prime Factor	Digits	Year
5548013	1509059537	10	~1989
5548339	55483391	8	~1985
5548457	44387657	8	~1985
5548619	11097239	8	~1984
5548811	11097623	8	~1984
5548843	399516697	9	~1987
5548897	33293383	8	~1985
5548937	44391497	8	~1985
5548999	55489991	8	~1985
5549051	11098103	8	~1984
5549189	44393513	8	~1985
5549189	77688647	8
5549393	33296359	8	~1985
5549587	99892567	8	~1986
5549591	11099183	8	~1984
5549617	33297703	8	~1985
5549657	44397257	8	~1985
5549891	11099783	8	~1984
5549927	932387737	9	~1988
5549977	33299863	8	~1985
5550059	11100119	8	~1984
5550439	55504391	8	~1985
5550529	222021161	9	~1987
5550683	11101367	8	~1984
5550733	33304399	8	~1985

5.680.769 digits

26-07-05