Small Mersenne Prime Factors (page 852/4665)

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
7721293	355179479	9	~1988
7721303	15442607	8	~1985
7721501	46329007	8	~1986
7721891	15443783	8	~1985
7721977	46331863	8	~1986
7722017	108108239	9	~1987
7722119	15444239	8	~1985
7722443	15444887	8	~1985
7722623	15445247	8	~1985
7722791	15445583	8	~1985
7722833	417032983	9	~1988
7722931	77229311	8	~1986
7723097	61784777	8	~1986
7723283	15446567	8	~1985
7723511	15447023	8	~1985
7723679	15447359	8	~1985
7723721	46342327	8	~1986
7723973	46343839	8	~1986
7723979	15447959	8	~1985
7724371	77243711	8	~1986
7724753	108146543	9	~1987
7724771	15449543	8	~1985
7724891	15449783	8	~1985
7725299	15450599	8	~1985
7725433	46352599	8	~1986

Exp.	Prime Factor	Digits	Year
7725611	15451223	8	~1985
7725709	2580386807	10	~1990
7725911	15451823	8	~1985
7725959	61807673	8	~1986
7726139	15452279	8	~1985
7726261	46357567	8	~1986
7726343	15452687	8	~1985
7726391	15452783	8	~1985
7726679	15453359	8	~1985
7727099	15454199	8	~1985
7727233	46363399	8	~1986
7727359	77273591	8	~1986
7728179	15456359	8	~1985
7728293	46369759	8	~1986
7728443	15456887	8	~1985
7728551	15457103	8	~1985
7729343	15458687	8	~1985
7729451	15458903	8	~1985
7729451	200965727	9
7729763	15459527	8	~1985
7729919	15459839	8	~1985
7730111	15460223	8	~1985
7730279	15460559	8	~1985
7730341	46382047	8	~1986
7730417	46382503	8	~1986

Exp.	Prime Factor	Digits	Year
7730431	123686897	9	~1987
7730531	15461063	8	~1985
7730651	200996927	9	~1987
7730963	695786671	9	~1989
7731433	46388599	8	~1986
7731707	432975593	9	~1988
7731721	46390327	8	~1986
7731761	46390567	8	~1986
7732321	46393927	8	~1986
7732457	46394743	8	~1986
7732471	77324711	8	~1986
7732633	46395799	8	~1986
7733087	61864697	8	~1986
7733431	77334311	8	~1986
7733471	15466943	8	~1985
7733711	15467423	8	~1985
7733941	46403647	8	~1986
7733951	61871609	8	~1986
7733983	77339831	8	~1986
7734119	15468239	8	~1985
7734203	15468407	8	~1985
7734317	61874537	8	~1986
7734607	139222927	9	~1987
7734689	61877513	8	~1986
7734791	15469583	8	~1985

Exp.	Prime Factor	Digits	Year
7734827	61878617	8	~1986
7734911	61879289	8	~1986
7734971	15469943	8	~1985
7735163	15470327	8	~1985
7735319	15470639	8	~1985
7735361	46412167	8	~1986
7735439	15470879	8	~1985
7735583	15471167	8	~1985
7735597	46413583	8	~1986
7735811	15471623	8	~1985
7736593	46419559	8	~1986
7736627	510617383	9	~1988
7736633	46419799	8	~1986
7736761	46420567	8	~1986
7736831	15473663	8	~1985
7736831	61894649	8
7736873	46421239	8	~1986
7736951	15473903	8	~1985
7737071	15474143	8	~1985
7737263	15474527	8	~1985
7737677	61901417	8	~1986
7737967	77379671	8	~1986
7738271	15476543	8	~1985
7738337	46430023	8	~1986
7738337	61906697	8

4.368.158 digits

24-10-27