Small Mersenne Prime Factors (page 870/5670)

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
7133879	57071033	8	~1986
7133957	57071657	8	~1986
7133963	14267927	8	~1985
7133969	57071753	8	~1986
7134107	57072857	8	~1986
7134119	14268239	8	~1985
7134131	14268263	8	~1985
7134181	214025431	9	~1987
7134251	14268503	8	~1985
7134341	42806047	8	~1986
7134601	42807607	8	~1986
7134661	156962543	9	~1987
7134767	57078137	8	~1986
7135061	42810367	8	~1986
7135199	57081593	8	~1986
7135217	57081737	8	~1986
7135379	14270759	8	~1985
7135391	14270783	8	~1985
7135559	14271119	8	~1985
7135577	99898079	8	~1987
7135643	14271287	8	~1985
7135813	42814879	8	~1986
7135853	42815119	8	~1986
7135901	42815407	8	~1986
7135949	57087593	8	~1986

Exp.	Prime Factor	Digits	Year
7136021	57088169	8	~1986
7136027	570882161	9	~1988
7136081	228354593	9	~1987
7136099	14272199	8	~1985
7136401	42818407	8	~1986
7136483	14272967	8	~1985
7136497	42818983	8	~1986
7136663	14273327	8	~1985
7136771	14273543	8	~1985
7136917	42821503	8	~1986
7137853	42827119	8	~1986
7137913	42827479	8	~1986
7138217	385463719	9	~1988
7138409	57107273	8	~1986
7138619	14277239	8	~1985
7138643	14277287	8	~1985
7138919	14277839	8	~1985
7139123	14278247	8	~1985
7139189	57113513	8	~1986
7139299	414079343	9	~1988
7139437	42836623	8	~1986
7139519	14279039	8	~1985
7139543	14279087	8	~1985
7139567	57116537	8	~1986
7139917	171358009	9	~1987

Exp.	Prime Factor	Digits	Year
7139933	99959063	8	~1987
7140047	57120377	8	~1986
7140047	171361129	9
7140251	14280503	8	~1985
7140299	14280599	8	~1985
7140383	14280767	8	~1985
7140403	71404031	8	~1986
7140677	57125417	8	~1986
7140767	171378409	9	~1987
7140911	14281823	8	~1985
7140911	57127289	8
7140923	14281847	8	~1985
7140997	42845983	8	~1986
7141009	214230271	9	~1987
7141103	14282207	8	~1985
7141153	171387673	9	~1987
7141361	57130889	8	~1986
7141451	14282903	8	~1985
7141643	14283287	8	~1985
7142011	114272177	9	~1987
7142039	14284079	8	~1985
7142299	71422991	8	~1986
7142321	42853927	8	~1986
7142699	14285399	8	~1985
7142743	71427431	8	~1986

Exp.	Prime Factor	Digits	Year
7142819	14285639	8	~1985
7142939	14285879	8	~1985
7143139	71431391	8	~1986
7143377	42860263	8	~1986
7143377	57147017	8
7143557	57148457	8	~1986
7143683	14287367	8	~1985
7143709	214311271	9	~1987
7143841	157164503	9	~1987
7143887	57151097	8	~1986
7144031	14288063	8	~1985
7144037	42864223	8	~1986
7144223	14288447	8	~1985
7144387	285775481	9	~1988
7144433	42866599	8	~1986
7144451	14288903	8	~1985
7144499	14288999	8	~1985
7144561	42867367	8	~1986
7144859	14289719	8	~1985
7144967	57159737	8	~1986
7144979	14289959	8	~1985
7145393	42872359	8	~1986
7145399	14290799	8	~1985
7145609	57164873	8	~1986
7145609	100038527	9

5.366.787 digits

26-02-08