Small Mersenne Prime Factors (page 947/5460)

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
8418779	16837559	8	~1985
8418803	16837607	8	~1985
8418863	16837727	8	~1985
8418913	50513479	8	~1986
8419069	202057657	9	~1988
8419121	50514727	8	~1986
8419181	67353449	8	~1987
8419783	84197831	8	~1987
8420183	16840367	8	~1985
8420317	50521903	8	~1986
8420393	50522359	8	~1986
8420519	16841039	8	~1985
8420519	67364153	8
8420651	16841303	8	~1985
8420677	50524063	8	~1986
8420837	50525023	8	~1986
8420843	16841687	8	~1985
8420891	67367129	8	~1987
8421071	16842143	8	~1985
8421733	1145355689	10	~1990
8421737	50530423	8	~1986
8421773	50530639	8	~1986
8421779	67374233	8	~1987
8421821	50530927	8	~1986
8421827	218967503	9	~1988

Exp.	Prime Factor	Digits	Year
8422019	16844039	8	~1985
8422039	202128937	9	~1988
8422181	67377449	8	~1987
8422763	16845527	8	~1985
8423117	67384937	8	~1987
8423231	16846463	8	~1985
8423321	67386569	8	~1987
8423333	50539999	8	~1986
8423797	50542783	8	~1986
8423903	16847807	8	~1985
8424077	50544463	8	~1986
8424593	117944303	9	~1987
8424599	67396793	8	~1987
8424817	50548903	8	~1986
8424869	67398953	8	~1987
8424973	50549839	8	~1986
8425553	10228621343	11	~1992
8425799	16851599	8	~1985
8425811	16851623	8	~1985
8425847	67406777	8	~1987
8426039	16852079	8	~1985
8426123	16852247	8	~1985
8426189	67409513	8	~1987
8426221	50557327	8	~1986
8426261	50557567	8	~1986

Exp.	Prime Factor	Digits	Year
8426393	50558359	8	~1986
8426591	16853183	8	~1985
8426647	337065881	9	~1988
8426731	84267311	8	~1987
8427491	16854983	8	~1985
8427539	16855079	8	~1985
8427599	16855199	8	~1985
8427701	50566207	8	~1986
8427707	67421657	8	~1987
8427833	269690657	9	~1988
8428163	16856327	8	~1985
8428169	117994367	9	~1987
8428289	67426313	8	~1987
8428307	202279369	9	~1988
8428319	67426553	8	~1987
8428333	50569999	8	~1986
8428487	151712767	9	~1987
8428601	50571607	8	~1986
8428631	16857263	8	~1985
8428633	50571799	8	~1986
8429243	16858487	8	~1985
8429257	50575543	8	~1986
8429341	50576047	8	~1986
8429423	16858847	8	~1985
8429767	84297671	8	~1987

Exp.	Prime Factor	Digits	Year
8430263	16860527	8	~1985
8430377	50582263	8	~1986
8430377	67443017	8
8430473	50582839	8	~1986
8430479	16860959	8	~1985
8430731	16861463	8	~1985
8431487	67451897	8	~1987
8431529	67452233	8	~1987
8431637	50589823	8	~1986
8431751	16863503	8	~1985
8431799	16863599	8	~1985
8431931	16863863	8	~1985
8432197	50593183	8	~1986
8432309	67458473	8	~1987
8432321	50593927	8	~1986
8432471	16864943	8	~1985
8432537	67460297	8	~1987
8432581	50595487	8	~1986
8432647	84326471	8	~1987
8432849	67462793	8	~1987
8433211	84332111	8	~1987
8433263	16866527	8	~1985
8433527	67468217	8	~1987
8433779	16867559	8	~1985
8433779	67470233	8

5.157.210 digits

25-11-02