Small Mersenne Prime Factors (page 609/5745)

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
3929417	23576503	8	~1984
3929479	39294791	8	~1984
3929531	7859063	7	~1983
3929581	86450783	8	~1985
3929657	23577943	8	~1984
3929729	149329703	9	~1986
3929741	23578447	8	~1984
3929957	31439657	8	~1984
3929977	23579863	8	~1984
3930221	31441769	8	~1984
3930271	70744879	8	~1985
3930331	62885297	8	~1985
3930517	94332409	8	~1985
3930541	117916231	9	~1985
3930611	7861223	7	~1983
3930613	62889809	8	~1985
3930683	7861367	7	~1983
3931087	70759567	8	~1985
3931261	62900177	8	~1985
3931349	55038887	8	~1985
3931379	31451033	8	~1984
3931463	7862927	7	~1983
3931517	31452137	8	~1984
3931523	7863047	7	~1983
3931649	31453193	8	~1984

Exp.	Prime Factor	Digits	Year
3931721	23590327	8	~1984
3931933	86502527	8	~1985
3932063	7864127	7	~1983
3932077	62913233	8	~1985
3932399	7864799	7	~1983
3932503	39325031	8	~1984
3932657	55057199	8	~1985
3932717	31461737	8	~1984
3932861	31462889	8	~1984
3933091	70795639	8	~1985
3933119	7866239	7	~1983
3933131	7866263	7	~1983
3933131	70796359	8
3933233	23599399	8	~1984
3933337	23600023	8	~1984
3933431	7866863	7	~1983
3933569	31468553	8	~1984
3933577	23601463	8	~1984
3933731	31469849	8	~1984
3933871	70809679	8	~1985
3934261	62948177	8	~1985
3934499	7868999	7	~1983
3934583	7869167	7	~1983
3934873	118046191	9	~1985
3935003	7870007	7	~1983

Exp.	Prime Factor	Digits	Year
3935117	23610703	8	~1984
3935257	62964113	8	~1985
3935411	7870823	7	~1983
3935411	283349593	9
3935417	23612503	8	~1984
3935471	7870943	7	~1983
3935627	31485017	8	~1984
3935719	39357191	8	~1984
3935759	7871519	7	~1983
3935879	31487033	8	~1984
3936007	39360071	8	~1984
3936043	157441721	9	~1986
3936271	39362711	8	~1984
3936301	62980817	8	~1985
3936577	62985233	8	~1985
3936683	7873367	7	~1983
3936899	7873799	7	~1983
3937019	7874039	7	~1983
3937561	23625367	8	~1984
3937567	39375671	8	~1984
3937771	39377711	8	~1984
3938087	70885567	8	~1985
3938257	94518169	8	~1985
3938303	7876607	7	~1983
3938303	94519273	8

Exp.	Prime Factor	Digits	Year
3938447	31507577	8	~1984
3938447	70892047	8
3938477	23630863	8	~1984
3938633	55140863	8	~1985
3938699	7877399	7	~1983
3938827	133920119	9	~1986
3939191	7878383	7	~1983
3939337	23636023	8	~1984
3939443	7878887	7	~1983
3939499	94547977	8	~1985
3939521	23637127	8	~1984
3939671	7879343	7	~1983
3939779	7879559	7	~1983
3939791	31518329	8	~1984
3939839	7879679	7	~1983
3939899	7879799	7	~1983
3939953	23639719	8	~1984
3939953	55159343	8
3940021	118200631	9	~1985
3940177	23641063	8	~1984
3940247	31521977	8	~1984
3940303	94567273	8	~1985
3940319	31522553	8	~1984
3940367	31522937	8	~1984
3940373	23642239	8	~1984

5.441.361 digits

26-03-15