Small Mersenne Prime Factors (page 995/5670)

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
8970133	53820799	8	~1986
8970497	53822983	8	~1986
8970497	125586959	9
8970503	233233079	9	~1988
8970757	53824543	8	~1986
8970791	717663281	9	~1989
8970959	71767673	8	~1987
8970979	161477623	9	~1988
8971037	71768297	8	~1987
8971139	17942279	8	~1985
8971177	143538833	9	~1988
8971181	53827087	8	~1986
8971241	53827447	8	~1986
8971499	17942999	8	~1985
8971559	17943119	8	~1985
8971663	89716631	8	~1987
8971757	71774057	8	~1987
8971811	161492599	9	~1988
8972101	53832607	8	~1986
8972291	17944583	8	~1985
8972963	17945927	8	~1985
8973131	17946263	8	~1985
8973311	17946623	8	~1985
8973343	143573489	9	~1988
8973401	53840407	8	~1986

Exp.	Prime Factor	Digits	Year
8973521	53841127	8	~1986
8973533	53841199	8	~1986
8973551	17947103	8	~1985
8973581	71788649	8	~1987
8973737	53842423	8	~1986
8973901	53843407	8	~1986
8974037	53844223	8	~1986
8974139	17948279	8	~1985
8974271	17948543	8	~1985
8974529	71796233	8	~1987
8974681	53848087	8	~1986
8975159	17950319	8	~1985
8975171	17950343	8	~1985
8975333	53851999	8	~1986
8975363	17950727	8	~1985
8975381	53852287	8	~1986
8975459	287214689	9	~1988
8975579	17951159	8	~1985
8975639	17951279	8	~1985
8975753	125660543	9	~1987
8975903	17951807	8	~1985
8976127	89761271	8	~1987
8976659	17953319	8	~1985
8976839	17953679	8	~1985
8977013	53862079	8	~1986

Exp.	Prime Factor	Digits	Year
8977039	89770391	8	~1987
8977201	53863207	8	~1986
8977271	17954543	8	~1985
8977379	17954759	8	~1985
8977571	17955143	8	~1985
8977571	71820569	8
8977679	17955359	8	~1985
8977721	53866327	8	~1986
8977763	17955527	8	~1985
8978171	17956343	8	~1985
8978323	89783231	8	~1987
8978381	53870287	8	~1986
8978663	17957327	8	~1985
8978759	17957519	8	~1985
8978831	17957663	8	~1985
8978891	17957783	8	~1985
8979359	17958719	8	~1985
8979371	71834969	8	~1987
8979611	17959223	8	~1985
8979857	53879143	8	~1986
8979923	17959847	8	~1985
8980109	125721527	9	~1987
8980319	17960639	8	~1985
8980429	197569439	9	~1988
8980441	143687057	9	~1988

Exp.	Prime Factor	Digits	Year
8980501	53883007	8	~1986
8980667	71845337	8	~1987
8980943	17961887	8	~1985
8981279	17962559	8	~1985
8981783	17963567	8	~1985
8981939	17963879	8	~1985
8982241	53893447	8	~1986
8982317	71858537	8	~1987
8982359	215576617	9	~1988
8982629	71861033	8	~1987
8982769	431172913	9	~1989
8982847	143725553	9	~1988
8982899	17965799	8	~1985
8983057	53898343	8	~1986
8983283	17966567	8	~1985
8983391	17966783	8	~1985
8983537	53901223	8	~1986
8983619	17967239	8	~1985
8983883	17967767	8	~1985
8984197	53905183	8	~1986
8984351	17968703	8	~1985
8984531	233597807	9	~1988
8984593	53907559	8	~1986
8984609	71876873	8	~1987
8984711	17969423	8	~1985

5.366.787 digits

26-02-08