Small Mersenne Prime Factors (page 339/5745)

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
1580713	37937113	8	~1982
1580759	3161519	7	~1979
1580849	60072263	8	~1983
1580851	66395743	8	~1983
1580897	9485383	7	~1981
1580921	98017103	8	~1983
1581071	3162143	7	~1979
1581071	12648569	8
1581157	47434711	8	~1982
1581311	3162623	7	~1979
1581317	12650537	8	~1981
1581487	25303793	8	~1982
1581533	9489199	7	~1981
1581577	9489463	7	~1981
1581623	3163247	7	~1979
1581737	9490423	7	~1981
1581743	3163487	7	~1979
1581757	9490543	7	~1981
1582151	3164303	7	~1979
1582151	28478719	8
1582159	15821591	8	~1981
1582159	63286361	8
1582247	12657977	8	~1981
1582267	15822671	8	~1981
1582267	28480807	8

Exp.	Prime Factor	Digits	Year
1582337	22152719	8	~1981
1582391	3164783	7	~1979
1582409	50637089	8	~1982
1582463	3164927	7	~1979
1582517	9495103	7	~1981
1582517	22155239	8
1582517	85455919	8
1582589	22156247	8	~1981
1582589	60138383	8
1582597	9495583	7	~1981
1582799	3165599	7	~1979
1582877	9497263	7	~1981
1582957	47488711	8	~1982
1582991	50655713	8	~1982
1583027	12664217	8	~1981
1583149	34829279	8	~1982
1583161	9498967	7	~1981
1583167	25330673	8	~1982
1583171	66493183	8	~1983
1583293	47498791	8	~1982
1583339	3166679	7	~1979
1583447	38002729	8	~1982
1583497	9500983	7	~1981
1583657	85517479	8	~1983
1583809	38011417	8	~1982

Exp.	Prime Factor	Digits	Year
1583843	3167687	7	~1979
1583861	9503167	7	~1981
1583863	243914903	9	~1984
1583917	25342673	8	~1982
1583999	3167999	7	~1979
1584017	12672137	8	~1981
1584031	139394729	9	~1983
1584047	12672377	8	~1981
1584059	3168119	7	~1979
1584083	3168167	7	~1979
1584139	15841391	8	~1981
1584169	63366761	8	~1983
1584269	50696609	8	~1982
1584371	12674969	8	~1981
1584403	25350449	8	~1982
1584431	3168863	7	~1979
1584431	12675449	8
1584491	3168983	7	~1979
1584571	76059409	8	~1983
1584623	3169247	7	~1979
1584629	12677033	8	~1981
1584701	9508207	7	~1981
1584881	202864769	9	~1984
1584901	34867823	8	~1982
1584931	215550617	9	~1984

Exp.	Prime Factor	Digits	Year
1584941	12679529	8	~1981
1584959	3169919	7	~1979
1584959	12679673	8
1584971	12679769	8	~1981
1585033	9510199	7	~1981
1585093	148998743	9	~1984
1585127	41213303	8	~1982
1585249	38045977	8	~1982
1585279	139504553	9	~1983
1585399	15853991	8	~1981
1585457	60247367	8	~1983
1585513	9513079	7	~1981
1585559	12684473	8	~1981
1585673	38056153	8	~1982
1585679	3171359	7	~1979
1585687	15856871	8	~1981
1585687	25370993	8
1585799	3171599	7	~1979
1585819	15858191	8	~1981
1585901	12687209	8	~1981
1585973	9515839	7	~1981
1586027	12688217	8	~1981
1586093	22205303	8	~1981
1586113	9516679	7	~1981
1586401	9518407	7	~1981

5.441.361 digits

26-03-15