Small Mersenne Prime Factors (page 737/5205)

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
5650829	45206633	8	~1985
5650937	45207497	8	~1985
5651069	79114967	8	~1986
5651171	45209369	8	~1985
5651183	11302367	8	~1984
5651279	11302559	8	~1984
5651297	45210377	8	~1985
5651603	11303207	8	~1984
5651771	11303543	8	~1984
5652067	56520671	8	~1985
5652341	33914047	8	~1985
5652683	11305367	8	~1984
5653001	33918007	8	~1985
5653181	45225449	8	~1985
5653211	45225689	8	~1985
5653493	33920959	8	~1985
5653523	11307047	8	~1984
5653577	33921463	8	~1985
5653601	33921607	8	~1985
5653643	11307287	8	~1984
5653751	11307503	8	~1984
5653799	11307599	8	~1984
5653807	90460913	8	~1986
5654447	101780047	9	~1986
5654503	90472049	8	~1986

Exp.	Prime Factor	Digits	Year
5654569	169637071	9	~1987
5654651	11309303	8	~1984
5654651	45237209	8
5654819	237502399	9	~1987
5654917	33929503	8	~1985
5655019	56550191	8	~1985
5655107	135722569	9	~1986
5655313	33931879	8	~1985
5655323	11310647	8	~1984
5655449	45243593	8	~1985
5655659	11311319	8	~1984
5655731	11311463	8	~1984
5655791	11311583	8	~1984
5655911	11311823	8	~1984
5656397	33938383	8	~1985
5656691	11313383	8	~1984
5656799	45254393	8	~1985
5656997	33941983	8	~1985
5657423	11314847	8	~1984
5657761	33946567	8	~1985
5657831	11315663	8	~1984
5658097	33948583	8	~1985
5658269	45266153	8	~1985
5658473	543213409	9	~1988
5658571	101854279	9	~1986

Exp.	Prime Factor	Digits	Year
5658623	11317247	8	~1984
5658781	33952687	8	~1985
5658899	11317799	8	~1984
5659091	11318183	8	~1984
5659163	11318327	8	~1984
5659211	11318423	8	~1984
5659237	531968279	9	~1988
5659343	11318687	8	~1984
5659373	33956239	8	~1985
5659469	79232567	8	~1986
5659931	11319863	8	~1984
5660003	11320007	8	~1984
5660033	79240463	8	~1986
5660101	33960607	8	~1985
5660203	56602031	8	~1985
5660243	316973609	9	~1987
5660411	11320823	8	~1984
5660579	11321159	8	~1984
5660591	11321183	8	~1984
5660663	11321327	8	~1984
5660717	33964303	8	~1985
5660801	33964807	8	~1985
5660951	11321903	8	~1984
5661083	11322167	8	~1984
5661209	79256927	8	~1986

Exp.	Prime Factor	Digits	Year
5661497	33968983	8	~1985
5661503	11323007	8	~1984
5661797	45294377	8	~1985
5661961	33971767	8	~1985
5661973	124563407	9	~1986
5662093	124566047	9	~1986
5662169	45297353	8	~1985
5662313	33973879	8	~1985
5662451	11324903	8	~1984
5662529	351076799	9	~1987
5662619	11325239	8	~1984
5662823	11325647	8	~1984
5662873	33977239	8	~1985
5662933	33977599	8	~1985
5662967	45303737	8	~1985
5663017	33978103	8	~1985
5663039	11326079	8	~1984
5663353	33980119	8	~1985
5663429	169902871	9	~1987
5663459	11326919	8	~1984
5663519	11327039	8	~1984
5663579	11327159	8	~1984
5663597	33981583	8	~1985
5664107	45312857	8	~1985
5664203	11328407	8	~1984

4.903.097 digits

25-07-08