Small Mersenne Prime Factors (page 358/5610)

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
1735277	24293879	8	~1982
1735421	10412527	8	~1981
1735421	13883369	8
1735423	17354231	8	~1981
1735463	3470927	7	~1980
1735477	10412863	8	~1981
1735499	41651977	8	~1982
1735529	222147713	9	~1984
1735579	17355791	8	~1981
1735703	3471407	7	~1980
1735823	3471647	7	~1980
1735931	13887449	8	~1981
1735961	10415767	8	~1981
1735997	13887977	8	~1981
1736029	93745567	8	~1983
1736099	13888793	8	~1981
1736153	41667673	8	~1982
1736173	302094103	9	~1984
1736177	52085311	8	~1983
1736191	31251439	8	~1982
1736197	27779153	8	~1982
1736219	31251943	8	~1982
1736233	10417399	8	~1981
1736393	55564577	8	~1983
1736519	3473039	7	~1980

Exp.	Prime Factor	Digits	Year
1736563	17365631	8	~1981
1736639	156297511	9	~1984
1736789	24315047	8	~1982
1736831	3473663	7	~1980
1736881	10421287	8	~1981
1736921	138953681	9	~1984
1736939	13895513	8	~1981
1737007	41688169	8	~1982
1737059	13896473	8	~1981
1737221	1139616977	10	~1986
1737311	3474623	7	~1980
1737371	83393809	8	~1983
1737521	10425127	8	~1981
1737599	281491039	9	~1984
1737677	13901417	8	~1981
1737691	156392191	9	~1984
1737773	10426639	8	~1981
1737899	3475799	7	~1980
1738019	13904153	8	~1981
1738019	55616609	8
1738043	3476087	7	~1980
1738171	17381711	8	~1981
1738211	3476423	7	~1980
1738307	31289527	8	~1982
1738391	3476783	7	~1980

Exp.	Prime Factor	Digits	Year
1738417	27814673	8	~1982
1738657	52159711	8	~1983
1738657	153001817	9
1738661	13909289	8	~1981
1738691	13909529	8	~1981
1738703	3477407	7	~1980
1738739	73027039	8	~1983
1738831	17388311	8	~1981
1738873	10433239	8	~1981
1738903	73033927	8	~1983
1738969	52169071	8	~1983
1739041	10434247	8	~1981
1739063	3478127	7	~1980
1739173	10435039	8	~1981
1739233	27827729	8	~1982
1739347	100882127	9	~1983
1739359	31308463	8	~1982
1739443	17394431	8	~1981
1739533	10437199	8	~1981
1739603	3479207	7	~1980
1739609	316608839	9	~1985
1739653	41751673	8	~1982
1739869	38277119	8	~1982
1739891	3479783	7	~1980
1739891	73075423	8

Exp.	Prime Factor	Digits	Year
1739911	17399111	8	~1981
1739957	13919657	8	~1981
1740041	177484183	9	~1984
1740187	69607481	8	~1983
1740241	10441447	8	~1981
1740257	13922057	8	~1981
1740259	17402591	8	~1981
1740293	24364103	8	~1982
1740367	17403671	8	~1981
1740379	41769097	8	~1982
1740379	59172887	8
1740503	3481007	7	~1980
1740691	184513247	9	~1984
1740701	52221031	8	~1983
1740731	3481463	7	~1980
1740779	3481559	7	~1980
1740811	69632441	8	~1983
1740881	10445287	8	~1981
1740911	3481823	7	~1980
1741013	41784313	8	~1982
1741079	3482159	7	~1980
1741079	13928633	8
1741099	31339783	8	~1982
1741241	10447447	8	~1981
1741339	17413391	8	~1981

5.307.017 digits

26-01-11