Small Mersenne Prime Factors (page 984/5730)

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
8750957	52505743	8	~1986
8751097	52506583	8	~1986
8751251	70010009	8	~1987
8751341	70010729	8	~1987
8751557	70012457	8	~1987
8752031	17504063	8	~1985
8752273	52513639	8	~1986
8752361	52514167	8	~1986
8752561	52515367	8	~1986
8752619	17505239	8	~1985
8752619	70020953	8
8752741	52516447	8	~1986
8752871	17505743	8	~1985
8753023	87530231	8	~1987
8753369	122547167	9	~1987
8753531	157563559	9	~1988
8753603	17507207	8	~1985
8753999	17507999	8	~1985
8754131	17508263	8	~1985
8754131	70033049	8
8754587	227619263	9	~1988
8754883	87548831	8	~1987
8755031	17510063	8	~1985
8755381	52532287	8	~1986
8755991	17511983	8	~1985

Exp.	Prime Factor	Digits	Year
8756063	17512127	8	~1985
8756393	52538359	8	~1986
8756401	52538407	8	~1986
8756437	52538623	8	~1986
8756557	52539343	8	~1986
8756591	17513183	8	~1985
8756983	210167593	9	~1988
8757041	52542247	8	~1986
8757263	17514527	8	~1985
8757713	52546279	8	~1986
8757851	17515703	8	~1985
8758157	52548943	8	~1986
8758171	140130737	9	~1987
8758199	17516399	8	~1985
8758201	52549207	8	~1986
8758229	70065833	8	~1987
8758577	70068617	8	~1987
8758583	17517167	8	~1985
8758637	52551823	8	~1986
8758733	52552399	8	~1986
8759183	17518367	8	~1985
8759279	17518559	8	~1985
8759353	262780591	9	~1988
8759357	70074857	8	~1987
8759603	17519207	8	~1985

Exp.	Prime Factor	Digits	Year
8759657	52557943	8	~1986
8759771	17519543	8	~1985
8759843	17519687	8	~1985
8759867	70078937	8	~1987
8759921	52559527	8	~1986
8759951	17519903	8	~1985
8760307	87603071	8	~1987
8760337	140165393	9	~1987
8760419	70083353	8	~1987
8760421	52562527	8	~1986
8760623	17521247	8	~1985
8760701	52564207	8	~1986
8760743	17521487	8	~1985
8761019	17522039	8	~1985
8761141	52566847	8	~1986
8761213	52567279	8	~1986
8761327	508156967	9	~1989
8761517	70092137	8	~1987
8761619	17523239	8	~1985
8762051	17524103	8	~1985
8762399	17524799	8	~1985
8762473	52574839	8	~1986
8762597	52575583	8	~1986
8762617	52575703	8	~1986
8762951	17525903	8	~1985

Exp.	Prime Factor	Digits	Year
8763239	17526479	8	~1985
8763353	52580119	8	~1986
8763383	17526767	8	~1985
8763749	70109993	8	~1987
8763763	87637631	8	~1987
8763803	17527607	8	~1985
8763971	17527943	8	~1985
8764331	17528663	8	~1985
8764499	17528999	8	~1985
8764577	52587463	8	~1986
8764621	52587727	8	~1986
8764787	70118297	8	~1987
8764859	17529719	8	~1985
8764933	52589599	8	~1986
8765063	17530127	8	~1985
8765173	52591039	8	~1986
8765741	262972231	9	~1988
8765789	70126313	8	~1987
8766113	122725583	9	~1987
8766223	140259569	9	~1987
8766503	17533007	8	~1985
8766899	17533799	8	~1985
8766941	263008231	9	~1988
8767001	70136009	8	~1987
8767061	70136489	8	~1987

5.426.516 digits

26-03-08