Small Mersenne Prime Factors (page 940/5460)

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
8317781	49906687	8	~1986
8318027	1197795889	10	~1990
8318069	66544553	8	~1987
8318197	332727881	9	~1988
8318231	16636463	8	~1985
8318279	16636559	8	~1985
8318291	16636583	8	~1985
8318417	49910503	8	~1986
8318477	49910863	8	~1986
8318537	49911223	8	~1986
8318591	16637183	8	~1985
8318657	49911943	8	~1986
8318657	665492561	9
8318759	16637519	8	~1985
8319037	49914223	8	~1986
8319221	66553769	8	~1987
8319257	66554057	8	~1987
8319263	16638527	8	~1985
8319419	399332113	9	~1988
8319581	49917487	8	~1986
8319677	66557417	8	~1987
8319803	16639607	8	~1985
8319943	133119089	9	~1987
8320097	66560777	8	~1987
8320159	149762863	9	~1987

Exp.	Prime Factor	Digits	Year
8320379	16640759	8	~1985
8320619	16641239	8	~1985
8321003	16642007	8	~1985
8321171	16642343	8	~1985
8321213	49927279	8	~1986
8321309	66570473	8	~1987
8321429	66571433	8	~1987
8321543	16643087	8	~1985
8321723	16643447	8	~1985
8321783	16643567	8	~1985
8321881	249656431	9	~1988
8321897	49931383	8	~1986
8322269	66578153	8	~1987
8322533	49935199	8	~1986
8322683	16645367	8	~1985
8322733	932146097	9	~1989
8322773	49936639	8	~1986
8323103	16646207	8	~1985
8323439	16646879	8	~1985
8323517	116529239	9	~1987
8323541	66588329	8	~1987
8323571	16647143	8	~1985
8323603	83236031	8	~1987
8323751	16647503	8	~1985
8323793	49942759	8	~1986

Exp.	Prime Factor	Digits	Year
8323817	49942903	8	~1986
8323823	16647647	8	~1985
8323883	16647767	8	~1985
8324411	16648823	8	~1985
8325071	16650143	8	~1985
8325227	216455903	9	~1988
8325437	66603497	8	~1987
8325491	16650983	8	~1985
8325539	16651079	8	~1985
8325599	16651199	8	~1985
8325671	16651343	8	~1985
8325893	266428577	9	~1988
8325899	16651799	8	~1985
8326033	49956199	8	~1986
8326079	16652159	8	~1985
8326267	83262671	8	~1987
8326511	16653023	8	~1985
8326553	49959319	8	~1986
8326727	66613817	8	~1987
8326793	49960759	8	~1986
8326861	49961167	8	~1986
8327191	83271911	8	~1987
8327233	49963399	8	~1986
8327279	16654559	8	~1985
8327533	49965199	8	~1986

Exp.	Prime Factor	Digits	Year
8327999	66623993	8	~1987
8328121	133249937	9	~1987
8328311	66626489	8	~1987
8328493	49970959	8	~1986
8328701	66629609	8	~1987
8328701	266518433	9
8328731	16657463	8	~1985
8329103	16658207	8	~1985
8329157	66633257	8	~1987
8329859	16659719	8	~1985
8329859	266555489	9
8329987	149939767	9	~1987
8330407	83304071	8	~1987
8330771	66646169	8	~1987
8330789	66646313	8	~1987
8330963	16661927	8	~1985
8330999	16661999	8	~1985
8331097	399892657	9	~1988
8331131	16662263	8	~1985
8331181	49987087	8	~1986
8331371	16662743	8	~1985
8331571	149968279	9	~1987
8331599	349927159	9	~1988
8331857	49991143	8	~1986
8331923	16663847	8	~1985

5.157.210 digits

25-11-02