Small Mersenne Prime Factors (page 507/5775)

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
2926909	70245817	8	~1984
2926919	5853839	7	~1982
2927101	46833617	8	~1984
2927219	5854439	7	~1982
2927459	23419673	8	~1983
2927473	17564839	8	~1983
2927473	70259353	8
2927537	40985519	8	~1984
2927591	5855183	7	~1982
2927711	23421689	8	~1983
2927713	46843409	8	~1984
2927789	23422313	8	~1983
2928049	87841471	8	~1984
2928083	5856167	7	~1982
2928089	40993247	8	~1984
2928119	5856239	7	~1982
2928173	17569039	8	~1983
2928203	5856407	7	~1982
2928361	17570167	8	~1983
2928361	46853777	8
2928479	70283497	8	~1984
2928509	23428073	8	~1983
2928547	70285129	8	~1984
2928691	29286911	8	~1983
2928791	5857583	7	~1982

Exp.	Prime Factor	Digits	Year
2929061	17574367	8	~1983
2929099	29290991	8	~1983
2929259	5858519	7	~1982
2929343	5858687	7	~1982
2929529	23436233	8	~1983
2929571	5859143	7	~1982
2929607	23436857	8	~1983
2929813	17578879	8	~1983
2929961	17579767	8	~1983
2930119	29301191	8	~1983
2930173	158229343	9	~1985
2930381	17582287	8	~1983
2930401	17582407	8	~1983
2930491	29304911	8	~1983
2930507	70332169	8	~1984
2930533	17583199	8	~1983
2930633	41028863	8	~1984
2930713	17584279	8	~1983
2930761	134815007	9	~1985
2930831	5861663	7	~1982
2930861	17585167	8	~1983
2931083	5862167	7	~1982
2931101	23448809	8	~1983
2931241	46899857	8	~1984
2931319	70351657	8	~1984

Exp.	Prime Factor	Digits	Year
2931637	17589823	8	~1983
2931847	99682799	8	~1985
2931941	17591647	8	~1983
2931961	46911377	8	~1984
2932031	5864063	7	~1982
2932067	70369609	8	~1984
2932343	5864687	7	~1982
2932577	23460617	8	~1983
2932703	5865407	7	~1982
2932871	93851873	8	~1984
2932931	5865863	7	~1982
2932981	17597887	8	~1983
2932999	70391977	8	~1984
2933023	46928369	8	~1984
2933083	46929329	8	~1984
2933267	52798807	8	~1984
2933291	52799239	8	~1984
2933311	29333111	8	~1983
2933479	70403497	8	~1984
2933531	5867063	7	~1982
2933677	17602063	8	~1983
2933717	23469737	8	~1983
2933759	70410217	8	~1984
2934091	52813639	8	~1984
2934311	5868623	7	~1982

Exp.	Prime Factor	Digits	Year
2934311	23474489	8
2934361	17606167	8	~1983
2934401	23475209	8	~1983
2934473	70427353	8	~1984
2934479	5868959	7	~1982
2934587	76299263	8	~1984
2934629	41084807	8	~1984
2934647	23477177	8	~1983
2934671	5869343	7	~1982
2934839	5869679	7	~1982
2934871	52827679	8	~1984
2934881	17609287	8	~1983
2934917	88047511	8	~1984
2934941	93918113	8	~1984
2935183	29351831	8	~1983
2935379	5870759	7	~1982
2935379	217218047	9
2935391	5870783	7	~1982
2935423	29354231	8	~1983
2935453	17612719	8	~1983
2935463	5870927	7	~1982
2935589	93938849	8	~1984
2935589	182006519	9
2935609	70454617	8	~1984
2935619	23484953	8	~1983

5.471.290 digits

26-03-29