Small Mersenne Prime Factors (page 339/6015)

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
1557593	9345559	7	~1981
1557623	65420167	8	~1983
1557733	9346399	7	~1981
1557763	24924209	8	~1982
1557869	46736071	8	~1982
1558079	3116159	7	~1979
1558087	15580871	8	~1981
1558103	3116207	7	~1979
1558213	146472023	9	~1983
1558223	3116447	7	~1979
1558409	46752271	8	~1982
1558523	187022761	9	~1984
1558559	3117119	7	~1979
1558597	9351583	7	~1981
1558771	252520903	9	~1984
1558811	3117623	7	~1979
1558811	28058599	8
1558841	12470729	8	~1981
1558867	90414287	8	~1983
1559017	74832817	8	~1983
1559113	9354679	7	~1981
1559161	9354967	7	~1981
1559171	3118343	7	~1979
1559297	12474377	8	~1981
1559303	3118607	7	~1979

Exp.	Prime Factor	Digits	Year
1559347	140341231	9	~1983
1559351	28068319	8	~1982
1559447	37426729	8	~1982
1559491	65498623	8	~1983
1559549	121644823	9	~1983
1559713	34313687	8	~1982
1559749	84226447	8	~1983
1559777	9358663	7	~1981
1559807	12478457	8	~1981
1559821	24957137	8	~1982
1559821	174699953	9
1559879	3119759	7	~1979
1559879	49916129	8
1559891	3119783	7	~1979
1559891	65515423	8
1560047	40561223	8	~1982
1560203	3120407	7	~1979
1560263	3120527	7	~1979
1560371	40569647	8	~1982
1560683	3121367	7	~1979
1560739	37457737	8	~1982
1560743	3121487	7	~1979
1560877	9365263	7	~1981
1560883	24974129	8	~1982
1560883	53070023	8

Exp.	Prime Factor	Digits	Year
1560893	9365359	7	~1981
1560901	9365407	7	~1981
1560913	9365479	7	~1981
1560913	37461913	8
1561139	3122279	7	~1979
1561463	3122927	7	~1979
1561519	15615191	8	~1981
1561541	9369247	7	~1981
1561607	74957137	8	~1983
1561697	9370183	7	~1981
1561823	65596567	8	~1983
1562051	3124103	7	~1979
1562063	3124127	7	~1979
1562081	9372487	7	~1981
1562107	37490569	8	~1982
1562159	12497273	8	~1981
1562359	28122463	8	~1982
1562417	9374503	7	~1981
1562447	12499577	8	~1981
1562471	3124943	7	~1979
1562531	150002977	9	~1983
1562591	3125183	7	~1979
1563097	9378583	7	~1981
1563119	3126239	7	~1979
1563143	37515433	8	~1982

Exp.	Prime Factor	Digits	Year
1563253	71909639	8	~1983
1563259	53150807	8	~1982
1563409	62536361	8	~1983
1563433	9380599	7	~1981
1563433	109440311	9
1563511	15635111	8	~1981
1563539	3127079	7	~1979
1563571	28144279	8	~1982
1563689	50038049	8	~1982
1563811	25020977	8	~1982
1563851	3127703	7	~1979
1563911	3127823	7	~1979
1563937	37534489	8	~1982
1563943	15639431	8	~1981
1563959	3127919	7	~1979
1563959	75070033	8
1564117	9384703	7	~1981
1564421	9386527	7	~1981
1564421	12515369	8
1564501	34419023	8	~1982
1564559	12516473	8	~1981
1564603	53196503	8	~1982
1564603	62584121	8
1564679	50069729	8	~1982
1564741	9388447	7	~1981

5.710.620 digits

26-07-19