Small Mersenne Prime Factors (page 384/5025)

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
2009881	12059287	8	~1981
2009923	20099231	8	~1982
2010053	12060319	8	~1981
2010061	44221343	8	~1983
2010083	4020167	7	~1980
2010227	16081817	8	~1982
2010311	4020623	7	~1980
2010467	16083737	8	~1982
2010571	20105711	8	~1982
2010583	48253993	8	~1983
2010667	80426681	8	~1983
2010689	16085513	8	~1982
2011003	32176049	8	~1982
2011019	48264457	8	~1983
2011127	498759497	9	~1985
2011183	868831057	9	~1986
2011193	28156703	8	~1982
2011391	4022783	7	~1980
2011441	12068647	8	~1981
2011517	16092137	8	~1982
2011631	4023263	7	~1980
2011637	12069823	8	~1981
2011637	16093097	8
2011673	209213993	9	~1984
2011753	32188049	8	~1982

Exp.	Prime Factor	Digits	Year
2011769	16094153	8	~1982
2011769	60353071	8
2011799	4023599	7	~1980
2012147	16097177	8	~1982
2012237	12073423	8	~1981
2012243	4024487	7	~1980
2012449	60373471	8	~1983
2012611	36226999	8	~1983
2012639	4025279	7	~1980
2012663	4025327	7	~1980
2012693	60380791	8	~1983
2012743	20127431	8	~1982
2012909	16103273	8	~1982
2013013	44286287	8	~1983
2013127	20131271	8	~1982
2013337	12080023	8	~1981
2013359	4026719	7	~1980
2013439	20134391	8	~1982
2013553	12081319	8	~1981
2013653	12081919	8	~1981
2013779	4027559	7	~1980
2013877	32222033	8	~1982
2013911	4027823	7	~1980
2014031	16112249	8	~1982
2014049	64449569	8	~1983

Exp.	Prime Factor	Digits	Year
2014081	273915017	9	~1985
2014139	4028279	7	~1980
2014139	64452449	8
2014217	12085303	8	~1981
2014297	12085783	8	~1981
2014303	20143031	8	~1982
2014333	12085999	8	~1981
2014333	1530893081	10
2014559	36262063	8	~1983
2014709	76558943	8	~1983
2014739	4029479	7	~1980
2014867	36267607	8	~1983
2014877	16119017	8	~1982
2014939	48358537	8	~1983
2014979	4029959	7	~1980
2015063	4030127	7	~1980
2015063	596458649	9
2015081	16120649	8	~1982
2015213	112851929	9	~1984
2015347	116890127	9	~1984
2015411	52400687	8	~1983
2015423	4030847	7	~1980
2015579	36280423	8	~1983
2015621	12093727	8	~1981
2015627	96750097	8	~1984

Exp.	Prime Factor	Digits	Year
2015731	20157311	8	~1982
2015771	4031543	7	~1980
2015771	145135513	9
2015791	32252657	8	~1982
2015879	4031759	7	~1980
2015941	145147753	9	~1984
2016137	28225919	8	~1982
2016137	403227401	9
2016193	12097159	8	~1981
2016419	4032839	7	~1980
2016583	32265329	8	~1982
2016583	68563823	8
2016671	4033343	7	~1980
2016823	32269169	8	~1982
2016977	16135817	8	~1982
2017019	36306343	8	~1983
2017027	48408649	8	~1983
2017109	16136873	8	~1982
2017109	108923887	9
2017133	12102799	8	~1981
2017289	28242047	8	~1982
2017333	12103999	8	~1981
2017403	149287823	9	~1984
2017403	161392241	9
2017469	60524071	8	~1983

4.724.182 digits

25-04-13