Small Mersenne Prime Factors (page 595/5670)

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
3807593	213225209	9	~1986
3807737	30461897	8	~1984
3807757	60924113	8	~1985
3807941	22847647	8	~1984
3808397	91401529	8	~1985
3808591	68554639	8	~1985
3808751	7617503	7	~1982
3808801	22852807	8	~1984
3808967	91415209	8	~1985
3808979	7617959	7	~1982
3809051	7618103	7	~1982
3809137	22854823	8	~1984
3809159	7618319	7	~1982
3809339	7618679	7	~1982
3809461	22856767	8	~1984
3809503	152380121	9	~1986
3809591	30476729	8	~1984
3809639	30477113	8	~1984
3809753	22858519	8	~1984
3809857	22859143	8	~1984
3809891	7619783	7	~1982
3809917	22859503	8	~1984
3809941	22859647	8	~1984
3809941	83818703	8
3810071	7620143	7	~1982

Exp.	Prime Factor	Digits	Year
3810083	7620167	7	~1982
3810097	22860583	8	~1984
3810409	83828999	8	~1985
3810409	152416361	9
3810413	22862479	8	~1984
3810419	7620839	7	~1982
3810497	182903857	9	~1986
3810511	60968177	8	~1985
3810553	22863319	8	~1984
3810563	160043647	9	~1986
3810643	60970289	8	~1985
3810733	22864399	8	~1984
3810899	7621799	7	~1982
3811217	22867303	8	~1984
3811289	53358047	8	~1984
3811331	7622663	7	~1982
3811627	152465081	9	~1986
3811657	22869943	8	~1984
3811681	152467241	9	~1986
3811771	60988337	8	~1985
3811949	30495593	8	~1984
3812191	38121911	8	~1984
3812219	7624439	7	~1982
3812309	30498473	8	~1984
3812357	91496569	8	~1985

Exp.	Prime Factor	Digits	Year
3812569	152502761	9	~1986
3812843	7625687	7	~1982
3813391	38133911	8	~1984
3813419	68641543	8	~1985
3813427	68641687	8	~1985
3813599	7627199	7	~1982
3813611	7627223	7	~1982
3813893	22883359	8	~1984
3813941	22883647	8	~1984
3813983	274606777	9	~1986
3814081	22884487	8	~1984
3814091	7628183	7	~1982
3814093	22884559	8	~1984
3814121	30512969	8	~1984
3814319	160201399	9	~1986
3814403	7628807	7	~1982
3814553	91549273	8	~1985
3814931	7629863	7	~1982
3814981	61039697	8	~1985
3815081	30520649	8	~1984
3815243	7630487	7	~1982
3815303	7630607	7	~1982
3815351	30522809	8	~1984
3815521	22893127	8	~1984
3815579	30524633	8	~1984

Exp.	Prime Factor	Digits	Year
3815639	7631279	7	~1982
3815681	114470431	9	~1985
3815761	22894567	8	~1984
3815891	7631783	7	~1982
3816107	91586569	8	~1985
3816149	30529193	8	~1984
3816167	30529337	8	~1984
3816277	22897663	8	~1984
3816497	664070479	9	~1987
3816557	30532457	8	~1984
3816677	30533417	8	~1984
3816691	68700439	8	~1985
3817111	221392439	9	~1986
3817193	22903159	8	~1984
3817259	7634519	7	~1982
3817393	22904359	8	~1984
3817753	22906519	8	~1984
3817757	114532711	9	~1985
3817859	190892951	9	~1986
3817859	740664647	9
3817939	68722903	8	~1985
3817981	22907887	8	~1984
3818021	30544169	8	~1984
3818071	152722841	9	~1986
3818077	61089233	8	~1985

5.366.787 digits

26-02-08