Small Mersenne Prime Factors (page 956/5460)

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
8549837	68398697	8	~1987
8550011	17100023	8	~1985
8550023	17100047	8	~1985
8550359	17100719	8	~1985
8550623	17101247	8	~1985
8550791	17101583	8	~1985
8550827	68406617	8	~1987
8551019	17102039	8	~1985
8551063	85510631	8	~1987
8551079	17102159	8	~1985
8551139	17102279	8	~1985
8551223	17102447	8	~1985
8551253	51307519	8	~1986
8551379	17102759	8	~1985
8551451	17102903	8	~1985
8551511	3437707423	10	~1991
8551759	205242217	9	~1988
8551997	51311983	8	~1986
8552279	17104559	8	~1985
8552353	51314119	8	~1986
8552363	17104727	8	~1985
8552471	17104943	8	~1985
8552519	68420153	8	~1987
8552737	51316423	8	~1986
8552939	68423513	8	~1987

Exp.	Prime Factor	Digits	Year
8553029	68424233	8	~1987
8553101	51318607	8	~1986
8553301	342132041	9	~1988
8553491	17106983	8	~1985
8553541	51321247	8	~1986
8553599	17107199	8	~1985
8553683	17107367	8	~1985
8553803	273721697	9	~1988
8554163	17108327	8	~1985
8554421	68435369	8	~1987
8554607	68436857	8	~1987
8554751	68438009	8	~1987
8554771	153985879	9	~1987
8554829	68438633	8	~1987
8555051	17110103	8	~1985
8555171	17110343	8	~1985
8555353	393546239	9	~1988
8555639	154001503	9	~1987
8555759	17111519	8	~1985
8555831	68446649	8	~1987
8556133	136898129	9	~1987
8556749	68453993	8	~1987
8556923	17113847	8	~1985
8556959	17113919	8	~1985
8557079	17114159	8	~1985

Exp.	Prime Factor	Digits	Year
8557169	68457353	8	~1987
8557229	68457833	8	~1987
8557573	51345439	8	~1986
8557691	17115383	8	~1985
8557931	17115863	8	~1985
8557931	838677239	9
8557937	68463497	8	~1987
8558233	51349399	8	~1986
8558261	51349567	8	~1986
8558477	119818679	9	~1987
8558867	68470937	8	~1987
8558899	85588991	8	~1987
8559179	17118359	8	~1985
8559539	17119079	8	~1985
8559563	17119127	8	~1985
8559569	68476553	8	~1987
8559767	821737633	9	~1989
8560289	68482313	8	~1987
8560327	136965233	9	~1987
8560463	17120927	8	~1985
8560753	51364519	8	~1986
8560859	17121719	8	~1985
8560907	68487257	8	~1987
8561341	51368047	8	~1986
8561479	85614791	8	~1987

Exp.	Prime Factor	Digits	Year
8561573	119862023	9	~1987
8561603	17123207	8	~1985
8562311	17124623	8	~1985
8562343	85623431	8	~1987
8562377	51374263	8	~1986
8562551	68500409	8	~1987
8562803	17125607	8	~1985
8562857	68502857	8	~1987
8563031	17126063	8	~1985
8563283	17126567	8	~1985
8563517	68508137	8	~1987
8563559	17127119	8	~1985
8563741	51382447	8	~1986
8563811	17127623	8	~1985
8563811	68510489	8
8564063	17128127	8	~1985
8564113	256923391	9	~1988
8564123	17128247	8	~1985
8564177	119898479	9	~1987
8564273	51385639	8	~1986
8564813	51388879	8	~1986
8565281	51391687	8	~1986
8565581	68524649	8	~1987
8565691	85656911	8	~1987
8565971	17131943	8	~1985

5.157.210 digits

25-11-02