Small Mersenne Prime Factors (page 679/5445)

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
4804571	9609143	7	~1983
4804979	9609959	7	~1983
4805231	9610463	7	~1983
4805267	38442137	8	~1985
4805621	38444969	8	~1985
4805657	28833943	8	~1984
4805711	9611423	7	~1983
4805903	9611807	7	~1983
4805903	153788897	9
4805939	9611879	7	~1983
4805959	48059591	8	~1985
4806071	9612143	7	~1983
4806181	221084327	9	~1987
4806211	230698129	9	~1987
4806377	28838263	8	~1984
4806437	413353583	9	~1987
4806463	48064631	8	~1985
4806523	307617473	9	~1987
4806541	807498889	9	~1988
4806673	28840039	8	~1984
4806863	9613727	7	~1983
4806871	346094713	9	~1987
4806899	153820769	9	~1986
4806917	38455337	8	~1985
4806947	38455577	8	~1985

Exp.	Prime Factor	Digits	Year
4806947	115366729	9
4806959	961391801	9	~1988
4807079	9614159	7	~1983
4807087	740291399	9	~1988
4807091	9614183	7	~1983
4807199	38457593	8	~1985
4807241	28843447	8	~1984
4807343	9614687	7	~1983
4807469	38459753	8	~1985
4807519	115380457	9	~1986
4807717	28846303	8	~1984
4807877	67310279	8	~1985
4808003	9616007	7	~1983
4808101	105778223	9	~1986
4808351	38466809	8	~1985
4808417	38467337	8	~1985
4808513	28851079	8	~1984
4808939	38471513	8	~1985
4809037	28854223	8	~1984
4809197	38473577	8	~1985
4809263	9618527	7	~1983
4809383	9618767	7	~1983
4809509	67333127	8	~1985
4809719	9619439	7	~1983
4809731	38477849	8	~1985

Exp.	Prime Factor	Digits	Year
4809859	48098591	8	~1985
4810199	9620399	7	~1983
4810217	28861303	8	~1984
4810343	9620687	7	~1983
4810501	28863007	8	~1984
4810721	28864327	8	~1984
4810867	76973873	8	~1985
4810901	28865407	8	~1984
4810913	67352783	8	~1985
4810987	86597767	8	~1986
4811159	38489273	8	~1985
4811159	86600863	8
4811447	38491577	8	~1985
4811507	38492057	8	~1985
4811777	38494217	8	~1985
4811783	9623567	7	~1983
4811909	67366727	8	~1985
4812179	9624359	7	~1983
4812239	9624479	7	~1983
4812299	9624599	7	~1983
4812307	48123071	8	~1985
4812329	721849351	9	~1988
4812349	105871679	9	~1986
4812383	9624767	7	~1983
4812413	28874479	8	~1984

Exp.	Prime Factor	Digits	Year
4812481	105874583	9	~1986
4812721	28876327	8	~1984
4812851	9625703	7	~1983
4813051	77008817	8	~1985
4813283	9626567	7	~1983
4813597	77017553	8	~1985
4813747	48137471	8	~1985
4813799	9627599	7	~1983
4813799	38510393	8
4813841	28883047	8	~1984
4814171	9628343	7	~1983
4814219	9628439	7	~1983
4814219	154055009	9
4814471	9628943	7	~1983
4814597	28887583	8	~1984
4814651	9629303	7	~1983
4814863	48148631	8	~1985
4814863	77037809	8
4814963	9629927	7	~1983
4815067	77041073	8	~1985
4815311	38522489	8	~1985
4815581	346721833	9	~1987
4815623	9631247	7	~1983
4815673	28894039	8	~1984
4815697	77051153	8	~1985

5.142.307 digits

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