Small Mersenne Prime Factors (page 755/5610)

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
5653807	90460913	8	~1986
5654447	101780047	9	~1986
5654503	90472049	8	~1986
5654549	79163687	8	~1986
5654569	169637071	9	~1987
5654651	11309303	8	~1984
5654651	45237209	8
5654819	237502399	9	~1987
5654917	33929503	8	~1985
5655019	56550191	8	~1985
5655107	135722569	9	~1986
5655313	33931879	8	~1985
5655323	11310647	8	~1984
5655449	45243593	8	~1985
5655659	11311319	8	~1984
5655731	11311463	8	~1984
5655791	11311583	8	~1984
5655911	11311823	8	~1984
5656397	33938383	8	~1985
5656691	11313383	8	~1984
5656759	101821663	9	~1986
5656799	45254393	8	~1985
5656997	33941983	8	~1985
5657423	11314847	8	~1984
5657761	33946567	8	~1985

Exp.	Prime Factor	Digits	Year
5657831	11315663	8	~1984
5658097	33948583	8	~1985
5658269	45266153	8	~1985
5658473	543213409	9	~1988
5658571	101854279	9	~1986
5658623	11317247	8	~1984
5658781	33952687	8	~1985
5658899	11317799	8	~1984
5659091	11318183	8	~1984
5659163	11318327	8	~1984
5659211	11318423	8	~1984
5659237	531968279	9	~1988
5659343	11318687	8	~1984
5659373	33956239	8	~1985
5659469	79232567	8	~1986
5659931	11319863	8	~1984
5660003	11320007	8	~1984
5660033	79240463	8	~1986
5660101	33960607	8	~1985
5660203	56602031	8	~1985
5660243	316973609	9	~1987
5660411	11320823	8	~1984
5660579	11321159	8	~1984
5660591	11321183	8	~1984
5660663	11321327	8	~1984

Exp.	Prime Factor	Digits	Year
5660717	33964303	8	~1985
5660801	33964807	8	~1985
5660951	11321903	8	~1984
5661083	11322167	8	~1984
5661209	79256927	8	~1986
5661497	33968983	8	~1985
5661503	11323007	8	~1984
5661797	45294377	8	~1985
5661961	33971767	8	~1985
5661973	124563407	9	~1986
5662093	124566047	9	~1986
5662169	45297353	8	~1985
5662313	33973879	8	~1985
5662451	11324903	8	~1984
5662529	351076799	9	~1987
5662619	11325239	8	~1984
5662823	11325647	8	~1984
5662873	33977239	8	~1985
5662933	33977599	8	~1985
5662967	45303737	8	~1985
5663017	33978103	8	~1985
5663039	11326079	8	~1984
5663353	33980119	8	~1985
5663429	169902871	9	~1987
5663459	11326919	8	~1984

Exp.	Prime Factor	Digits	Year
5663519	11327039	8	~1984
5663579	11327159	8	~1984
5663597	33981583	8	~1985
5664107	45312857	8	~1985
5664203	11328407	8	~1984
5664427	56644271	8	~1985
5664563	11329127	8	~1984
5664779	11329559	8	~1984
5665043	11330087	8	~1984
5665151	45321209	8	~1985
5665259	11330519	8	~1984
5665259	45322073	8
5665277	33991663	8	~1985
5665631	11331263	8	~1984
5665853	79321943	8	~1986
5666093	79325303	8	~1986
5666249	45329993	8	~1985
5666483	11332967	8	~1984
5666561	33999367	8	~1985
5666711	11333423	8	~1984
5666821	34000927	8	~1985
5666833	34000999	8	~1985
5666971	3094166167	10	~1990
5667071	11334143	8	~1984
5667217	532718399	9	~1988

5.307.017 digits

26-01-11