Small Mersenne Prime Factors (page 931/5025)

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
8611703	17223407	8	~1985
8612221	51673327	8	~1986
8612399	6011454503	10	~1991
8612711	17225423	8	~1985
8613041	51678247	8	~1986
8613127	137810033	9	~1987
8613677	51682063	8	~1986
8613743	17227487	8	~1985
8613953	51683719	8	~1986
8614031	17228063	8	~1985
8614079	68912633	8	~1987
8614093	465161023	9	~1989
8614157	51684943	8	~1986
8614253	51685519	8	~1986
8614297	51685783	8	~1986
8614297	1705630807	10
8614337	68914697	8	~1987
8614439	17228879	8	~1985
8614477	51686863	8	~1986
8614499	17228999	8	~1985
8614831	86148311	8	~1987
8614873	258446191	9	~1988
8614901	68919209	8	~1987
8615137	137842193	9	~1987
8615231	17230463	8	~1985

Exp.	Prime Factor	Digits	Year
8615261	51691567	8	~1986
8615543	17231087	8	~1985
8615891	17231783	8	~1985
8616131	17232263	8	~1985
8616281	68930249	8	~1987
8616373	51698239	8	~1986
8616407	68931257	8	~1987
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

Exp.	Prime Factor	Digits	Year
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
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

Exp.	Prime Factor	Digits	Year
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
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

4.724.182 digits

25-04-13