Small Mersenne Prime Factors (page 269/5850)

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
1107923	2215847	7	~1978
1108007	126312799	9	~1983
1108147	26595529	8	~1981
1108241	201699863	9	~1983
1108259	2216519	7	~1978
1108363	70935233	8	~1982
1108369	24384119	8	~1981
1108423	44336921	8	~1981
1108559	8868473	7	~1980
1108571	2217143	7	~1978
1108579	11085791	8	~1980
1108609	24389399	8	~1981
1108693	6652159	7	~1979
1108697	6652183	7	~1979
1108729	26609497	8	~1981
1108759	11087591	8	~1980
1108957	26614969	8	~1981
1109113	6654679	7	~1979
1109117	8872937	7	~1980
1109159	2218319	7	~1978
1109219	2218439	7	~1978
1109243	35495777	8	~1981
1109291	2218583	7	~1978
1109291	106491937	9
1109363	28843439	8	~1981

Exp.	Prime Factor	Digits	Year
1109579	19972423	8	~1981
1109629	24411839	8	~1981
1109639	2219279	7	~1978
1109839	11098391	8	~1980
1109881	6659287	7	~1979
1109897	8879177	7	~1980
1109903	2219807	7	~1978
1110007	11100071	8	~1980
1110089	266421361	9	~1983
1110133	6660799	7	~1979
1110133	24422927	8
1110269	35528609	8	~1981
1110367	37752479	8	~1981
1110413	35533217	8	~1981
1110449	33313471	8	~1981
1110479	19988623	8	~1981
1110523	17768369	8	~1980
1110547	17768753	8	~1980
1110713	15549983	8	~1980
1110817	26659609	8	~1981
1110959	26663017	8	~1981
1110971	2221943	7	~1978
1110973	6665839	7	~1979
1110979	91100279	8	~1982
1110983	73324879	8	~1982

Exp.	Prime Factor	Digits	Year
1111057	71107649	8	~1982
1111247	8889977	7	~1980
1111247	53339857	8
1111283	2222567	7	~1978
1111301	35561633	8	~1981
1111379	8891033	7	~1980
1111427	8891417	7	~1980
1111547	20007847	8	~1981
1111559	2223119	7	~1978
1111573	17785169	8	~1980
1111577	6669463	7	~1979
1111637	33349111	8	~1981
1111651	44466041	8	~1981
1111651	144514631	9
1111703	2223407	7	~1978
1111853	15565943	8	~1980
1111963	11119631	8	~1980
1111991	2223983	7	~1978
1112047	20016847	8	~1981
1112087	26690089	8	~1981
1112107	20017927	8	~1981
1112113	184610759	9	~1983
1112143	17794289	8	~1980
1112239	20020303	8	~1981
1112339	2224679	7	~1978

Exp.	Prime Factor	Digits	Year
1112351	8898809	7	~1980
1112359	37820207	8	~1981
1112359	44494361	8
1112389	246950359	9	~1983
1112483	73423879	8	~1982
1112519	2225039	7	~1978
1112591	2225183	7	~1978
1112663	26703913	8	~1981
1112677	33380311	8	~1981
1112677	44507081	8
1112729	35607329	8	~1981
1112897	8903177	7	~1980
1113011	2226023	7	~1978
1113137	8905097	7	~1980
1113193	6679159	7	~1979
1113197	15584759	8	~1980
1113239	2226479	7	~1978
1113239	8905913	7
1113373	17813969	8	~1980
1113401	53443249	8	~1982
1113403	71257793	8	~1982
1113557	8908457	7	~1980
1113557	220484287	9
1113713	6682279	7	~1979
1113719	2227439	7	~1978

5.546.121 digits

26-05-03