Small Mersenne Prime Factors (page 330/5730)

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
1519499	3038999	7	~1979
1519499	12155993	8
1519619	27353143	8	~1982
1519631	3039263	7	~1979
1519631	12157049	8
1519667	12157337	8	~1981
1519901	413413073	9	~1984
1519951	27359119	8	~1982
1520083	51682823	8	~1982
1520173	45605191	8	~1982
1520347	97302209	8	~1983
1520483	3040967	7	~1979
1520579	109481689	9	~1983
1520639	3041279	7	~1979
1520693	21289703	8	~1981
1520759	12166073	8	~1981
1520777	45623311	8	~1982
1520947	24335153	8	~1981
1521011	3042023	7	~1979
1521067	24337073	8	~1981
1521241	24339857	8	~1981
1521479	3042959	7	~1979
1521491	85203497	8	~1983
1521563	39560639	8	~1982
1521589	401699497	9	~1984

Exp.	Prime Factor	Digits	Year
1521623	3043247	7	~1979
1521677	9130063	7	~1980
1521853	219146833	9	~1984
1522019	63924799	8	~1983
1522063	15220631	8	~1981
1522187	27399367	8	~1982
1522331	3044663	7	~1979
1522387	24358193	8	~1981
1522483	36539593	8	~1982
1522541	48721313	8	~1982
1522727	182727241	9	~1984
1522771	109639513	9	~1983
1522799	3045599	7	~1979
1522841	9137047	7	~1980
1523099	255880633	9	~1984
1523101	9138607	7	~1980
1523161	9138967	7	~1980
1523297	9139783	7	~1980
1523377	73122097	8	~1983
1523393	9140359	7	~1980
1523407	15234071	8	~1981
1523581	33518783	8	~1982
1523653	9141919	7	~1980
1523653	33520367	8
1523663	3047327	7	~1979

Exp.	Prime Factor	Digits	Year
1523701	9142207	7	~1980
1523783	3047567	7	~1979
1523783	48761057	8
1523917	70100183	8	~1983
1523981	9143887	7	~1980
1524023	3048047	7	~1979
1524059	12192473	8	~1981
1524179	3048359	7	~1979
1524241	118890799	9	~1983
1524247	24387953	8	~1981
1524253	9145519	7	~1980
1524293	36583033	8	~1982
1524361	9146167	7	~1980
1524431	3048863	7	~1979
1524449	121955921	9	~1983
1524569	12196553	8	~1981
1524587	12196697	8	~1981
1524637	9147823	7	~1980
1524683	36592393	8	~1982
1524811	15248111	8	~1981
1524839	3049679	7	~1979
1524871	24397937	8	~1982
1524931	24398897	8	~1982
1525157	9150943	7	~1980
1525267	219638449	9	~1984

Exp.	Prime Factor	Digits	Year
1525297	9151783	7	~1980
1525333	45759991	8	~1982
1525421	9152527	7	~1980
1525633	9153799	7	~1980
1526053	24416849	8	~1982
1526093	21365303	8	~1981
1526267	36630409	8	~1982
1526297	9157783	7	~1980
1526363	3052727	7	~1979
1526377	61055081	8	~1982
1526557	36637369	8	~1982
1526587	51903959	8	~1982
1526639	3053279	7	~1979
1526641	33586103	8	~1982
1526873	9161239	7	~1980
1526873	36644953	8
1527023	3054047	7	~1979
1527083	3054167	7	~1979
1527121	33596663	8	~1982
1527443	113030783	9	~1983
1527523	51935783	8	~1982
1527563	64157647	8	~1983
1527563	1762807703	10
1527629	36663097	8	~1982
1527761	9166567	7	~1980

5.426.516 digits

26-03-08