Small Mersenne Prime Factors (page 538/5025)

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
3413411	6826823	7	~1982
3413759	6827519	7	~1982
3413789	47793047	8	~1984
3413831	27310649	8	~1983
3414011	6828023	7	~1982
3414163	34141631	8	~1984
3414227	27313817	8	~1983
3414287	27314297	8	~1983
3414311	6828623	7	~1982
3414337	20486023	8	~1983
3414421	20486527	8	~1983
3414457	20486743	8	~1983
3414457	102433711	9
3414527	61461487	8	~1984
3414581	20487487	8	~1983
3414883	34148831	8	~1984
3415261	20491567	8	~1983
3415679	6831359	7	~1982
3415697	20494183	8	~1983
3415697	27325577	8
3415757	20494543	8	~1983
3415781	27326249	8	~1983
3415883	6831767	7	~1982
3415897	20495383	8	~1983
3415931	6831863	7	~1982

Exp.	Prime Factor	Digits	Year
3416051	6832103	7	~1982
3416111	6832223	7	~1982
3416279	6832559	7	~1982
3416389	163986673	9	~1985
3416459	27331673	8	~1983
3416641	20499847	8	~1983
3416683	34166831	8	~1984
3416731	34167311	8	~1984
3416797	902034409	9	~1987
3416999	6833999	7	~1982
3417143	6834287	7	~1982
3417487	61514767	8	~1984
3417503	6835007	7	~1982
3417847	82028329	8	~1985
3417893	20507359	8	~1983
3417899	27343193	8	~1983
3417907	34179071	8	~1984
3418087	34180871	8	~1984
3418913	47864783	8	~1984
3418931	6837863	7	~1982
3418931	27351449	8
3418997	27351977	8	~1983
3419033	47866463	8	~1984
3419243	6838487	7	~1982
3419321	20515927	8	~1983

Exp.	Prime Factor	Digits	Year
3419531	191493737	9	~1986
3419653	20517919	8	~1983
3419707	34197071	8	~1984
3420083	6840167	7	~1982
3420253	20521519	8	~1983
3420341	27362729	8	~1983
3420457	20522743	8	~1983
3420617	47888639	8	~1984
3420631	34206311	8	~1984
3420787	61574167	8	~1984
3420821	20524927	8	~1983
3421079	6842159	7	~1982
3421513	75273287	8	~1985
3421633	20529799	8	~1983
3421679	6843359	7	~1982
3421793	47905103	8	~1984
3421853	328497889	9	~1986
3422017	102660511	9	~1985
3422137	20532823	8	~1983
3422143	34221431	8	~1984
3422207	27377657	8	~1983
3422227	34222271	8	~1984
3422231	6844463	7	~1982
3422437	54758993	8	~1984
3422437	82138489	8

Exp.	Prime Factor	Digits	Year
3422483	6844967	7	~1982
3422543	6845087	7	~1982
3422651	6845303	7	~1982
3422651	27381209	8
3422723	82145353	8	~1985
3422753	20536519	8	~1983
3422987	171149351	9	~1985
3423143	143772007	9	~1985
3423191	6846383	7	~1982
3423271	143777383	9	~1985
3423419	6846839	7	~1982
3423611	6847223	7	~1982
3423631	143792503	9	~1985
3423659	6847319	7	~1982
3423683	6847367	7	~1982
3423863	6847727	7	~1982
3423899	61630183	8	~1984
3424063	136962521	9	~1985
3424073	47937023	8	~1984
3424151	109572833	9	~1985
3424207	34242071	8	~1984
3424243	82181833	8	~1985
3424307	27394457	8	~1983
3424397	82185529	8	~1985
3424459	34244591	8	~1984

4.724.182 digits

25-04-13