Small Mersenne Prime Factors (page 406/5745)

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
2085833	29201663	8	~1982
2085841	83433641	8	~1984
2085869	29202167	8	~1982
2085899	4171799	7	~1980
2085971	4171943	7	~1980
2085983	4171967	7	~1980
2086043	4172087	7	~1980
2086079	4172159	7	~1980
2086127	37550287	8	~1983
2086321	12517927	8	~1982
2086361	12518167	8	~1982
2086433	12518599	8	~1982
2086589	62597671	8	~1983
2086739	4173479	7	~1980
2087051	4174103	7	~1980
2087081	66786593	8	~1983
2087233	196199903	9	~1984
2087303	4174607	7	~1980
2087303	505127327	9
2087483	4174967	7	~1980
2087489	317298329	9	~1985
2087531	4175063	7	~1980
2087759	4175519	7	~1980
2087831	4175663	7	~1980
2087983	70991423	8	~1983

Exp.	Prime Factor	Digits	Year
2087983	83519321	8
2088077	12528463	8	~1982
2088077	62642311	8
2088139	338278519	9	~1985
2088227	50117449	8	~1983
2088241	62647231	8	~1983
2088301	62649031	8	~1983
2088367	20883671	8	~1982
2088421	246433679	9	~1985
2088431	4176863	7	~1980
2088497	12530983	8	~1982
2088577	33417233	8	~1983
2088631	37595359	8	~1983
2088679	20886791	8	~1982
2088787	50130889	8	~1983
2088829	83553161	8	~1984
2088971	16711769	8	~1982
2089117	12534703	8	~1982
2089177	50140249	8	~1983
2089271	4178543	7	~1980
2089391	16715129	8	~1982
2089397	29251559	8	~1982
2089441	12536647	8	~1982
2089511	4179023	7	~1980
2089831	87772903	8	~1984

Exp.	Prime Factor	Digits	Year
2089873	133751873	9	~1984
2090069	16720553	8	~1982
2090069	568498769	9
2090071	33441137	8	~1983
2090119	20901191	8	~1982
2090177	79426727	8	~1983
2090203	20902031	8	~1982
2090353	96156239	8	~1984
2090477	12542863	8	~1982
2090489	16723913	8	~1982
2090689	112897207	9	~1984
2090821	12544927	8	~1982
2090873	50180953	8	~1983
2091149	66916769	8	~1983
2091281	200762977	9	~1984
2091283	20912831	8	~1982
2091431	4182863	7	~1980
2091497	29280959	8	~1982
2091503	4183007	7	~1980
2091581	12549487	8	~1982
2091587	16732697	8	~1982
2091599	4183199	7	~1980
2091703	33467249	8	~1983
2091773	12550639	8	~1982
2091839	16734713	8	~1982

Exp.	Prime Factor	Digits	Year
2091863	4183727	7	~1980
2091863	150614137	9
2091983	4183967	7	~1980
2092043	4184087	7	~1980
2092073	12552439	8	~1982
2092073	29289023	8
2092229	50213497	8	~1983
2092273	33476369	8	~1983
2092351	37662319	8	~1983
2092427	16739417	8	~1982
2092481	12554887	8	~1982
2092543	87886807	8	~1984
2092693	62780791	8	~1983
2092759	71153807	8	~1983
2092823	50227753	8	~1983
2092919	50230057	8	~1983
2092997	29301959	8	~1982
2093243	4186487	7	~1980
2093297	12559783	8	~1982
2093359	83734361	8	~1984
2093411	4186823	7	~1980
2093417	16747337	8	~1982
2093537	16748297	8	~1982
2093699	4187399	7	~1980
2093783	17977220839	11	~1989

5.441.361 digits

26-03-15