Small Mersenne Prime Factors (page 930/5730)

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
7948151	15896303	8	~1985
7948261	47689567	8	~1986
7948393	47690359	8	~1986
7948487	63587897	8	~1986
7948513	47691079	8	~1986
7948529	63588233	8	~1986
7948543	79485431	8	~1987
7948691	63589529	8	~1986
7948931	15897863	8	~1985
7948991	15897983	8	~1985
7949171	15898343	8	~1985
7949171	763120417	9
7949317	47695903	8	~1986
7949411	15898823	8	~1985
7949537	63596297	8	~1986
7949759	15899519	8	~1985
7950197	47701183	8	~1986
7950251	15900503	8	~1985
7950311	15900623	8	~1985
7950347	143106247	9	~1987
7950359	15900719	8	~1985
7950419	15900839	8	~1985
7950451	79504511	8	~1987
7950541	47703247	8	~1986
7950707	63605657	8	~1986

Exp.	Prime Factor	Digits	Year
7950791	15901583	8	~1985
7951103	15902207	8	~1985
7951201	47707207	8	~1986
7951211	15902423	8	~1985
7951301	63610409	8	~1986
7951403	15902807	8	~1985
7951523	15903047	8	~1985
7951681	47710087	8	~1986
7951711	79517111	8	~1987
7951751	63614009	8	~1986
7952099	15904199	8	~1985
7952171	63617369	8	~1986
7952363	15904727	8	~1985
7952389	4962290737	10	~1991
7952471	15904943	8	~1985
7952677	47716063	8	~1986
7953079	190873897	9	~1988
7953109	699873593	9	~1989
7953133	572625577	9	~1989
7953347	63626777	8	~1986
7953359	15906719	8	~1985
7953677	302239727	9	~1988
7953899	15907799	8	~1985
7953923	15907847	8	~1985
7954031	15908063	8	~1985

Exp.	Prime Factor	Digits	Year
7954979	397748951	9	~1988
7955117	1400100593	10	~1990
7955279	63642233	8	~1986
7955543	15911087	8	~1985
7955741	63645929	8	~1986
7955897	47735383	8	~1986
7956031	461449799	9	~1988
7956521	47739127	8	~1986
7956737	47740423	8	~1986
7956983	15913967	8	~1985
7957039	79570391	8	~1987
7957091	63656729	8	~1986
7957259	254632289	9	~1988
7957387	127318193	9	~1987
7957801	47746807	8	~1986
7957867	79578671	8	~1987
7958039	15916079	8	~1985
7958257	127332113	9	~1987
7958399	15916799	8	~1985
7958591	15917183	8	~1985
7958837	63670697	8	~1986
7959011	143262199	9	~1987
7959073	47754439	8	~1986
7959089	111427247	9	~1987
7959599	15919199	8	~1985

Exp.	Prime Factor	Digits	Year
7959599	63676793	8
7960019	15920039	8	~1985
7960223	15920447	8	~1985
7960363	127365809	9	~1987
7960453	47762719	8	~1986
7960523	15921047	8	~1985
7960559	15921119	8	~1985
7960643	15921287	8	~1985
7960699	79606991	8	~1987
7960969	1464818297	10	~1990
7961143	334368007	9	~1988
7961279	15922559	8	~1985
7961839	79618391	8	~1987
7961879	15923759	8	~1985
7961939	15923879	8	~1985
7962151	79621511	8	~1987
7962161	63697289	8	~1986
7962203	15924407	8	~1985
7962497	302574887	9	~1988
7962917	47777503	8	~1986
7963141	47778847	8	~1986
7963271	15926543	8	~1985
7963271	398163551	9
7963441	11849600209	11	~1992
7963523	15927047	8	~1985

5.426.516 digits

26-03-08