Small Mersenne Prime Factors (page 347/5025)

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
1721773	27548369	8	~1982
1721807	13774457	8	~1981
1721887	30993967	8	~1982
1722173	24110423	8	~1982
1722181	10333087	8	~1981
1722191	44776967	8	~1982
1722323	3444647	7	~1980
1722431	31003759	8	~1982
1722443	55118177	8	~1983
1722463	27559409	8	~1982
1722599	3445199	7	~1980
1722619	41342857	8	~1982
1722667	31008007	8	~1982
1722667	68906681	8
1722883	17228831	8	~1981
1723333	10339999	8	~1981
1723619	31025143	8	~1982
1723747	58607399	8	~1983
1723751	3447503	7	~1980
1723807	17238071	8	~1981
1723837	10343023	8	~1981
1723973	24135623	8	~1982
1723991	44823767	8	~1982
1724027	13792217	8	~1981
1724201	13793609	8	~1981

Exp.	Prime Factor	Digits	Year
1724209	41381017	8	~1982
1724309	24140327	8	~1982
1724329	41383897	8	~1982
1724351	3448703	7	~1980
1724357	24140999	8	~1982
1724399	3448799	7	~1980
1724399	541461287	9
1724473	51734191	8	~1983
1724641	27594257	8	~1982
1724669	51740071	8	~1983
1724677	1569456071	10	~1986
1724699	82785553	8	~1983
1724923	17249231	8	~1981
1724981	10349887	8	~1981
1725127	41403049	8	~1982
1725133	10350799	8	~1981
1725197	13801577	8	~1981
1725287	13802297	8	~1981
1725359	3450719	7	~1980
1725481	51764431	8	~1983
1725539	3451079	7	~1980
1725539	13804313	8
1725541	10353247	8	~1981
1725671	13805369	8	~1981
1725743	41417833	8	~1982

Exp.	Prime Factor	Digits	Year
1725781	51773431	8	~1983
1725833	176034967	9	~1984
1726139	3452279	7	~1980
1726159	31070863	8	~1982
1726303	17263031	8	~1981
1726327	27621233	8	~1982
1726379	3452759	7	~1980
1726477	82870897	8	~1983
1726489	37982759	8	~1982
1726513	10359079	8	~1981
1726577	10359463	8	~1981
1726661	10359967	8	~1981
1726757	65616767	8	~1983
1726811	3453623	7	~1980
1726859	3453719	7	~1980
1726883	3453767	7	~1980
1726897	10361383	8	~1981
1726931	13815449	8	~1981
1726993	93257623	8	~1983
1727263	17272631	8	~1981
1727317	27637073	8	~1982
1727339	3454679	7	~1980
1727437	10364623	8	~1981
1727483	3454967	7	~1980
1727513	10365079	8	~1981

Exp.	Prime Factor	Digits	Year
1727743	17277431	8	~1981
1727989	466557031	9	~1985
1728193	27651089	8	~1982
1728439	31111903	8	~1982
1728527	31113487	8	~1982
1728583	17285831	8	~1981
1728659	3457319	7	~1980
1728827	86441351	8	~1983
1728983	3457967	7	~1980
1728983	41495593	8
1729043	3458087	7	~1980
1729103	3458207	7	~1980
1729109	13832873	8	~1981
1729109	24207527	8
1729141	27666257	8	~1982
1729249	83003953	8	~1983
1729391	3458783	7	~1980
1729487	13835897	8	~1981
1729499	3458999	7	~1980
1729709	13837673	8	~1981
1729711	27675377	8	~1982
1729789	51893671	8	~1983
1729841	55354913	8	~1983
1729921	83036209	8	~1983
1729943	3459887	7	~1980

4.724.182 digits

25-04-13