Small Mersenne Prime Factors (page 905/4665)

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
8616599	17233199	8	~1985
8616719	17233439	8	~1985
8617211	17234423	8	~1985
8617373	275755937	9	~1988
8617391	17234783	8	~1985
8618063	17236127	8	~1985
8618251	137892017	9	~1987
8618591	17237183	8	~1985
8618639	17237279	8	~1985
8618699	17237399	8	~1985
8618783	17237567	8	~1985
8618893	51713359	8	~1986
8619067	758477897	9	~1989
8619077	51714463	8	~1986
8619421	51716527	8	~1986
8619431	17238863	8	~1985
8619683	17239367	8	~1985
8619791	17239583	8	~1985
8621051	17242103	8	~1985
8621147	68969177	8	~1987
8621339	17242679	8	~1985
8621551	155187919	9	~1987
8621773	51730639	8	~1986
8621939	68975513	8	~1987
8621983	86219831	8	~1987

Exp.	Prime Factor	Digits	Year
8622011	17244023	8	~1985
8622023	17244047	8	~1985
8622359	17244719	8	~1985
8622611	17245223	8	~1985
8622793	51736759	8	~1986
8622923	17245847	8	~1985
8622959	17245919	8	~1985
8623019	206952457	9	~1988
8623031	17246063	8	~1985
8623319	17246639	8	~1985
8623523	17247047	8	~1985
8623799	68990393	8	~1987
8624129	68993033	8	~1987
8624201	51745207	8	~1986
8624633	206991193	9	~1988
8624773	51748639	8	~1986
8624921	68999369	8	~1987
8625077	51750463	8	~1986
8625131	17250263	8	~1985
8625173	51751039	8	~1986
8625203	17250407	8	~1985
8625359	17250719	8	~1985
8625521	51753127	8	~1986
8625959	17251919	8	~1985
8625973	51755839	8	~1986

Exp.	Prime Factor	Digits	Year
8626043	17252087	8	~1985
8626603	138025649	9	~1987
8626621	51759727	8	~1986
8626823	17253647	8	~1985
8626831	86268311	8	~1987
8627351	69018809	8	~1987
8627357	51764143	8	~1986
8627357	69018857	8
8627533	51765199	8	~1986
8627603	17255207	8	~1985
8627639	17255279	8	~1985
8627813	51766879	8	~1986
8627903	17255807	8	~1985
8628131	17256263	8	~1985
8628149	120794087	9	~1987
8628677	207088249	9	~1988
8628773	120802823	9	~1987
8628923	17257847	8	~1985
8629139	17258279	8	~1985
8629739	17259479	8	~1985
8629763	17259527	8	~1985
8629813	51778879	8	~1986
8630177	51781063	8	~1986
8630243	17260487	8	~1985
8630519	17261039	8	~1985

Exp.	Prime Factor	Digits	Year
8630591	17261183	8	~1985
8630641	51783847	8	~1986
8631017	51786103	8	~1986
8631251	17262503	8	~1985
8631599	17263199	8	~1985
8631851	17263703	8	~1985
8632081	51792487	8	~1986
8632139	17264279	8	~1985
8632223	17264447	8	~1985
8632297	138116753	9	~1987
8632391	17264783	8	~1985
8632451	224443727	9	~1988
8632457	69059657	8	~1987
8632489	189914759	9	~1988
8632901	69063209	8	~1987
8632979	17265959	8	~1985
8633063	17266127	8	~1985
8633189	120864647	9	~1987
8633231	17266463	8	~1985
8633363	17266727	8	~1985
8633377	51800263	8	~1986
8633711	17267423	8	~1985
8633921	51803527	8	~1986
8634077	51804463	8	~1986
8634371	17268743	8	~1985

4.368.158 digits

24-10-27