Small Mersenne Prime Factors (page 347/5340)

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
1681219	30261943	8	~1982
1681259	3362519	7	~1980
1681321	80703409	8	~1983
1681517	10089103	8	~1981
1681573	10089439	8	~1981
1681619	53811809	8	~1983
1681661	10089967	8	~1981
1681661	53813153	8
1681717	80722417	8	~1983
1681817	50454511	8	~1982
1681837	10091023	8	~1981
1681853	50455591	8	~1982
1681957	10091743	8	~1981
1682111	3364223	7	~1980
1682237	10093423	8	~1981
1682363	3364727	7	~1980
1682383	16823831	8	~1981
1682399	3364799	7	~1980
1682407	26918513	8	~1982
1682413	50472391	8	~1982
1682477	952281983	9	~1986
1682557	131239447	9	~1984
1682671	26922737	8	~1982
1682809	37021799	8	~1982
1682831	80775889	8	~1983

Exp.	Prime Factor	Digits	Year
1683239	13465913	8	~1981
1683491	3366983	7	~1980
1683589	40406137	8	~1982
1683601	10101607	8	~1981
1683631	16836311	8	~1981
1683971	3367943	7	~1980
1684031	30312559	8	~1982
1684229	13473833	8	~1981
1684229	202107481	9
1684337	10106023	8	~1981
1684679	53909729	8	~1983
1684691	30324439	8	~1982
1684741	10108447	8	~1981
1684883	3369767	7	~1980
1684937	10109623	8	~1981
1684937	13479497	8
1684937	23589119	8
1684979	3369959	7	~1980
1685111	852666167	9	~1985
1685209	107853377	9	~1983
1685317	10111903	8	~1981
1685429	64046303	8	~1983
1685459	3370919	7	~1980
1685477	10112863	8	~1981
1685483	3370967	7	~1980

Exp.	Prime Factor	Digits	Year
1685543	43824119	8	~1982
1685549	23597687	8	~1982
1685591	3371183	7	~1980
1685759	3371519	7	~1980
1685837	144981983	9	~1984
1685917	91039519	8	~1983
1685933	40462393	8	~1982
1685953	158479583	9	~1984
1686109	107910977	9	~1983
1686203	3372407	7	~1980
1686257	10117543	8	~1981
1686287	13490297	8	~1981
1686403	229350809	9	~1984
1686473	10118839	8	~1981
1686491	3372983	7	~1980
1686551	3373103	7	~1980
1686647	13493177	8	~1981
1686677	40480249	8	~1982
1686857	10121143	8	~1981
1686913	10121479	8	~1981
1687583	3375167	7	~1980
1687627	16876271	8	~1981
1687627	27002033	8
1687633	10125799	8	~1981
1687643	3375287	7	~1980

Exp.	Prime Factor	Digits	Year
1687657	40503769	8	~1982
1687739	3375479	7	~1980
1687759	16877591	8	~1981
1687783	16877831	8	~1981
1687799	3375599	7	~1980
1687859	3375719	7	~1980
1687859	135028721	9
1688047	16880471	8	~1981
1688143	67525721	8	~1983
1688153	104665487	9	~1983
1688231	3376463	7	~1980
1688243	3376487	7	~1980
1688261	131684359	9	~1984
1688279	3376559	7	~1980
1688311	70909063	8	~1983
1688327	13506617	8	~1981
1688411	3376823	7	~1980
1688411	30391399	8
1688471	3376943	7	~1980
1688497	27015953	8	~1982
1688509	37147199	8	~1982
1688623	57413183	8	~1983
1688651	3377303	7	~1980
1688837	13510697	8	~1981
1688903	3377807	7	~1980

5.037.460 digits

25-09-07