Small Mersenne Prime Factors (page 927/5370)

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
8197823	16395647	8	~1985
8197921	49187527	8	~1986
8198009	114772127	9	~1987
8198459	147572263	9	~1987
8198639	16397279	8	~1985
8198717	49192303	8	~1986
8198759	16397519	8	~1985
8198759	65590073	8
8198783	16397567	8	~1985
8198789	65590313	8	~1986
8198843	16397687	8	~1985
8198951	16397903	8	~1985
8199371	16398743	8	~1985
8199553	49197319	8	~1986
8199623	16399247	8	~1985
8199791	16399583	8	~1985
8199791	65598329	8
8199827	147596887	9	~1987
8200013	49200079	8	~1986
8200061	65600489	8	~1986
8200091	16400183	8	~1985
8200217	49201303	8	~1986
8200433	49202599	8	~1986
8200463	16400927	8	~1985
8200741	49204447	8	~1986

Exp.	Prime Factor	Digits	Year
8201111	16402223	8	~1985
8201339	16402679	8	~1985
8201807	65614457	8	~1986
8201813	49210879	8	~1986
8201971	82019711	8	~1987
8202263	16404527	8	~1985
8202431	16404863	8	~1985
8202479	16404959	8	~1985
8202613	49215679	8	~1986
8202989	65623913	8	~1986
8203147	82031471	8	~1987
8203297	49219783	8	~1986
8203319	16406639	8	~1985
8203511	1394596871	10	~1990
8203691	16407383	8	~1985
8203883	16407767	8	~1985
8203901	49223407	8	~1986
8204017	49224103	8	~1986
8204033	49224199	8	~1986
8204101	49224607	8	~1986
8204113	131265809	9	~1987
8204177	49225063	8	~1986
8204191	131267057	9	~1987
8204281	131268497	9	~1987
8204737	49228423	8	~1986

Exp.	Prime Factor	Digits	Year
8204783	16409567	8	~1985
8205011	65640089	8	~1986
8205221	508723703	9	~1989
8205251	16410503	8	~1985
8205437	65643497	8	~1986
8205529	9452769409	10	~1992
8205623	16411247	8	~1985
8206619	16413239	8	~1985
8206799	16413599	8	~1985
8207027	459593513	9	~1989
8207051	16414103	8	~1985
8207471	16414943	8	~1985
8207483	16414967	8	~1985
8207627	147737287	9	~1987
8208037	49248223	8	~1986
8208143	16416287	8	~1985
8208311	16416623	8	~1985
8208439	82084391	8	~1987
8208757	49252543	8	~1986
8208797	65670377	8	~1986
8208911	16417823	8	~1985
8209031	16418063	8	~1985
8209277	197022649	9	~1988
8209703	16419407	8	~1985
8209837	197036089	9	~1988

Exp.	Prime Factor	Digits	Year
8210063	16420127	8	~1985
8210141	65681129	8	~1986
8210159	16420319	8	~1985
8210309	65682473	8	~1986
8210387	65683097	8	~1986
8210437	49262623	8	~1986
8210519	16421039	8	~1985
8210627	65685017	8	~1986
8210767	131372273	9	~1987
8210819	197059657	9	~1988
8210837	65686697	8	~1986
8211103	4729595329	10	~1991
8211163	131378609	9	~1987
8211167	197068009	9	~1988
8211191	16422383	8	~1985
8211383	16422767	8	~1985
8211503	16423007	8	~1985
8211719	16423439	8	~1985
8211877	49271263	8	~1986
8212019	16424039	8	~1985
8212091	16424183	8	~1985
8212157	65697257	8	~1986
8212363	82123631	8	~1987
8212511	16425023	8	~1985
8212703	16425407	8	~1985

5.067.432 digits

25-09-22