Small Mersenne Prime Factors (page 646/5745)

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
4320383	8640767	7	~1983
4320443	8640887	7	~1983
4320521	34564169	8	~1984
4320643	43206431	8	~1985
4320793	69132689	8	~1985
4320817	25924903	8	~1984
4320857	25925143	8	~1984
4320919	43209191	8	~1985
4321259	8642519	7	~1983
4321357	25928143	8	~1984
4321397	34571177	8	~1984
4321483	69143729	8	~1985
4321613	25929679	8	~1984
4321643	8643287	7	~1983
4321817	25930903	8	~1984
4322117	25932703	8	~1984
4322117	34576937	8
4322663	8645327	7	~1983
4322891	77812039	8	~1985
4322909	34583273	8	~1984
4322909	60520727	8
4322963	8645927	7	~1983
4323239	8646479	7	~1983
4323239	34585913	8
4323251	8646503	7	~1983

Exp.	Prime Factor	Digits	Year
4323337	25940023	8	~1984
4323337	69173393	8
4323359	8646719	7	~1983
4323401	25940407	8	~1984
4323503	8647007	7	~1983
4323589	337239943	9	~1987
4324157	242152793	9	~1986
4324297	25945783	8	~1984
4324417	69190673	8	~1985
4324543	43245431	8	~1985
4324561	25947367	8	~1984
4324631	34597049	8	~1984
4324669	129740071	9	~1986
4325117	25950703	8	~1984
4325159	8650319	7	~1983
4325267	34602137	8	~1984
4325333	25951999	8	~1984
4325351	8650703	7	~1983
4325389	337380343	9	~1987
4325417	34603337	8	~1984
4325473	69207569	8	~1985
4325593	25953559	8	~1984
4325969	60563567	8	~1985
4326011	8652023	7	~1983
4326071	8652143	7	~1983

Exp.	Prime Factor	Digits	Year
4326071	34608569	8
4326131	8652263	7	~1983
4326137	103827289	9	~1985
4326271	69220337	8	~1985
4326383	8652767	7	~1983
4326671	8653343	7	~1983
4326677	60573479	8	~1985
4326757	69228113	8	~1985
4326797	60575159	8	~1985
4326901	69230417	8	~1985
4326979	43269791	8	~1985
4327019	8654039	7	~1983
4327123	43271231	8	~1985
4327153	25962919	8	~1984
4327331	8654663	7	~1983
4327363	43273631	8	~1985
4327451	34619609	8	~1984
4327493	25964959	8	~1984
4327501	25965007	8	~1984
4327643	8655287	7	~1983
4327777	727066537	9	~1988
4327859	8655719	7	~1983
4328059	43280591	8	~1985
4328309	164475743	9	~1986
4328341	25970047	8	~1984

Exp.	Prime Factor	Digits	Year
4328459	8656919	7	~1983
4328711	8657423	7	~1983
4328783	8657567	7	~1983
4328833	69261329	8	~1985
4328843	8657687	7	~1983
4328969	129869071	9	~1986
4329011	77922199	8	~1985
4329079	43290791	8	~1985
4329097	25974583	8	~1984
4329191	8658383	7	~1983
4329257	34634057	8	~1984
4329263	8658527	7	~1983
4329277	103902649	9	~1985
4329907	43299071	8	~1985
4329907	69278513	8
4329937	25979623	8	~1984
4329953	60619343	8	~1985
4329977	103919449	9	~1985
4330099	43300991	8	~1985
4330457	60626399	8	~1985
4330493	25982959	8	~1984
4330493	60626903	8
4330507	43305071	8	~1985
4330511	34644089	8	~1984
4330523	8661047	7	~1983

5.441.361 digits

26-03-15