Small Mersenne Prime Factors (page 976/5460)

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
8861159	17722319	8	~1985
8861291	17722583	8	~1985
8861393	53168359	8	~1986
8861423	17722847	8	~1985
8861519	17723039	8	~1985
8861561	70892489	8	~1987
8861773	53170639	8	~1986
8861921	53171527	8	~1986
8861921	70895369	8
8862041	53172247	8	~1986
8862323	17724647	8	~1985
8862611	17725223	8	~1985
8862619	88626191	8	~1987
8862977	70903817	8	~1987
8863013	53178079	8	~1986
8863319	70906553	8	~1987
8863333	53179999	8	~1986
8863499	17726999	8	~1985
8863619	17727239	8	~1985
8863691	17727383	8	~1985
8863703	17727407	8	~1985
8864117	70912937	8	~1987
8864291	17728583	8	~1985
8864351	17728703	8	~1985
8864417	53186503	8	~1986

Exp.	Prime Factor	Digits	Year
8864461	53186767	8	~1986
8864903	17729807	8	~1985
8864969	336868823	9	~1988
8865011	17730023	8	~1985
8865011	70920089	8
8865203	17730407	8	~1985
8865443	17730887	8	~1985
8865583	212773993	9	~1988
8865763	141852209	9	~1987
8865803	17731607	8	~1985
8865991	88659911	8	~1987
8866079	17732159	8	~1985
8866079	70928633	8
8866147	88661471	8	~1987
8866391	17732783	8	~1985
8866463	17732927	8	~1985
8866603	88666031	8	~1987
8866667	70933337	8	~1987
8866943	17733887	8	~1985
8867003	17734007	8	~1985
8867657	70941257	8	~1987
8867773	53206639	8	~1986
8867861	70942889	8	~1987
8868479	17736959	8	~1985
8868803	17737607	8	~1985

Exp.	Prime Factor	Digits	Year
8868971	17737943	8	~1985
8869043	17738087	8	~1985
8869153	53214919	8	~1986
8869321	53215927	8	~1986
8869361	53216167	8	~1986
8869607	70956857	8	~1987
8869633	53217799	8	~1986
8869669	195132719	9	~1988
8869741	266092231	9	~1988
8869799	159656383	9	~1988
8869919	70959353	8	~1987
8870021	53220127	8	~1986
8870369	70962953	8	~1987
8870423	17740847	8	~1985
8870783	17741567	8	~1985
8870819	212899657	9	~1988
8871091	88710911	8	~1987
8871251	17742503	8	~1985
8871427	2430770999	10	~1990
8871701	53230207	8	~1986
8871893	53231359	8	~1986
8871899	17743799	8	~1985
8872153	53232919	8	~1986
8872621	53235727	8	~1986
8872631	70981049	8	~1987

Exp.	Prime Factor	Digits	Year
8872679	17745359	8	~1985
8872723	212945353	9	~1988
8872739	17745479	8	~1985
8872891	141966257	9	~1987
8872901	53237407	8	~1986
8872973	53237839	8	~1986
8873273	53239639	8	~1986
8873519	17747039	8	~1985
8873591	17747183	8	~1985
8873597	53241583	8	~1986
8873701	53242207	8	~1986
8873783	17747567	8	~1985
8873897	70991177	8	~1987
8874143	17748287	8	~1985
8874157	53244943	8	~1986
8874269	70994153	8	~1987
8874301	195234623	9	~1988
8874659	70997273	8	~1987
8874791	851979937	9	~1989
8874863	17749727	8	~1985
8874913	53249479	8	~1986
8874977	53249863	8	~1986
8875211	17750423	8	~1985
8875253	284008097	9	~1988
8875277	53251663	8	~1986

5.157.210 digits

25-11-02