Small Mersenne Prime Factors (page 828/5460)

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
6689399	53515193	8	~1986
6689537	53516297	8	~1986
6689537	93653519	8
6689623	66896231	8	~1986
6689699	53517593	8	~1986
6689723	13379447	8	~1984
6689741	40138447	8	~1985
6689999	13379999	8	~1984
6690059	13380119	8	~1984
6690119	13380239	8	~1984
6690863	13381727	8	~1984
6691079	53528633	8	~1986
6691277	40147663	8	~1985
6691337	40148023	8	~1985
6691403	13382807	8	~1984
6691481	40148887	8	~1985
6691891	66918911	8	~1986
6692051	53536409	8	~1986
6692173	40153039	8	~1985
6692183	374762249	9	~1988
6692197	160612729	9	~1987
6692341	147231503	9	~1987
6692593	40155559	8	~1985
6692669	53541353	8	~1986
6692771	13385543	8	~1984

Exp.	Prime Factor	Digits	Year
6692923	66929231	8	~1986
6693083	13386167	8	~1984
6693307	66933071	8	~1986
6693419	13386839	8	~1984
6693539	13387079	8	~1984
6693931	66939311	8	~1986
6693941	53551529	8	~1986
6694019	53552153	8	~1986
6694217	40165303	8	~1985
6694309	200829271	9	~1987
6694393	749772017	9	~1989
6694463	13388927	8	~1984
6694511	53556089	8	~1986
6694643	13389287	8	~1984
6694693	147283247	9	~1987
6694823	13389647	8	~1984
6694871	13389743	8	~1984
6694879	964062577	9	~1989
6694997	53559977	8	~1986
6695153	40170919	8	~1985
6695393	40172359	8	~1985
6695981	40175887	8	~1985
6696023	13392047	8	~1984
6696083	13392167	8	~1984
6696091	66960911	8	~1986

Exp.	Prime Factor	Digits	Year
6696293	40177759	8	~1985
6696331	66963311	8	~1986
6696383	13392767	8	~1984
6696451	66964511	8	~1986
6696779	13393559	8	~1984
6696787	66967871	8	~1986
6696857	93755999	8	~1986
6696923	13393847	8	~1984
6697157	40182943	8	~1985
6697193	40183159	8	~1985
6697241	40183447	8	~1985
6697283	13394567	8	~1984
6697441	40184647	8	~1985
6697511	13395023	8	~1984
6697591	66975911	8	~1986
6697619	321485713	9	~1988
6697721	40186327	8	~1985
6697721	53581769	8
6697759	66977591	8	~1986
6697897	40187383	8	~1985
6698053	40188319	8	~1985
6698339	13396679	8	~1984
6698383	66983831	8	~1986
6698807	53590457	8	~1986
6698903	13397807	8	~1984

Exp.	Prime Factor	Digits	Year
6699367	66993671	8	~1986
6699401	53595209	8	~1986
6699541	40197247	8	~1985
6699703	66997031	8	~1986
6699743	13399487	8	~1984
6699839	13399679	8	~1984
6699907	66999071	8	~1986
6699941	40199647	8	~1985
6699947	53599577	8	~1986
6700231	107203697	9	~1987
6700237	40201423	8	~1985
6700937	53607497	8	~1986
6700997	53607977	8	~1986
6700997	93813959	8
6701003	13402007	8	~1984
6701339	13402679	8	~1984
6701377	40208263	8	~1985
6701413	40208479	8	~1985
6701641	40209847	8	~1985
6701759	13403519	8	~1984
6701803	442318999	9	~1988
6701837	53614697	8	~1986
6702191	13404383	8	~1984
6702197	40213183	8	~1985
6702239	53617913	8	~1986

5.157.210 digits

25-11-02