Small Mersenne Prime Factors (page 884/5205)

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
7692287	61538297	8	~1986
7692617	61540937	8	~1986
7692623	15385247	8	~1985
7692731	15385463	8	~1985
7692977	61543817	8	~1986
7693243	76932431	8	~1986
7693331	15386663	8	~1985
7693403	15386807	8	~1985
7693597	123097553	9	~1987
7693667	61549337	8	~1986
7693739	61549913	8	~1986
7694003	15388007	8	~1985
7694237	61553897	8	~1986
7694539	76945391	8	~1986
7694651	15389303	8	~1985
7694663	15389327	8	~1985
7694917	46169503	8	~1986
7695629	61565033	8	~1986
7695859	76958591	8	~1986
7695871	138525679	9	~1987
7696079	15392159	8	~1985
7696127	61569017	8	~1986
7696411	138535399	9	~1987
7696511	61572089	8	~1986
7696679	15393359	8	~1985

Exp.	Prime Factor	Digits	Year
7696951	76969511	8	~1986
7697219	15394439	8	~1985
7697303	15394607	8	~1985
7697351	15394703	8	~1985
7697639	15395279	8	~1985
7697741	46186447	8	~1986
7697771	15395543	8	~1985
7697843	15395687	8	~1985
7698043	184753033	9	~1987
7698113	46188679	8	~1986
7698193	123171089	9	~1987
7698539	15397079	8	~1985
7698737	46192423	8	~1986
7699073	46194439	8	~1986
7699259	61594073	8	~1986
7699403	15398807	8	~1985
7699561	169390343	9	~1987
7699633	46197799	8	~1986
7699739	15399479	8	~1985
7699781	61598249	8	~1986
7699823	15399647	8	~1985
7699961	46199767	8	~1986
7700117	46200703	8	~1986
7700351	15400703	8	~1985
7700639	15401279	8	~1985

Exp.	Prime Factor	Digits	Year
7700717	61605737	8	~1986
7700753	46204519	8	~1986
7700831	15401663	8	~1985
7701131	15402263	8	~1985
7701623	15403247	8	~1985
7701721	677751449	9	~1989
7701817	46210903	8	~1986
7701847	123229553	9	~1987
7701977	46211863	8	~1986
7702199	15404399	8	~1985
7702271	61618169	8	~1986
7702379	15404759	8	~1985
7702433	46214599	8	~1986
7702451	15404903	8	~1985
7702451	61619609	8
7702511	15405023	8	~1985
7702763	15405527	8	~1985
7702811	15405623	8	~1985
7703309	61626473	8	~1986
7703609	61628873	8	~1986
7703621	61628969	8	~1986
7703671	77036711	8	~1986
7703963	15407927	8	~1985
7704071	15408143	8	~1985
7704083	15408167	8	~1985

Exp.	Prime Factor	Digits	Year
7704217	46225303	8	~1986
7704331	77043311	8	~1986
7704449	61635593	8	~1986
7704457	46226743	8	~1986
7704803	15409607	8	~1985
7704841	46229047	8	~1986
7704913	46229479	8	~1986
7705031	15410063	8	~1985
7705079	61640633	8	~1986
7705283	15410567	8	~1985
7705601	61644809	8	~1986
7705937	107883119	9	~1987
7706063	15412127	8	~1985
7706119	77061191	8	~1986
7706459	15412919	8	~1985
7706561	431567417	9	~1988
7706717	46240303	8	~1986
7706753	231202591	9	~1988
7706843	15413687	8	~1985
7707053	46242319	8	~1986
7707269	184974457	9	~1987
7707587	184982089	9	~1987
7707797	292896287	9	~1988
7707923	15415847	8	~1985
7709033	46254199	8	~1986

4.903.097 digits

25-07-08