Small Mersenne Prime Factors (page 915/5610)

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
7828559	62628473	8	~1986
7828939	78289391	8	~1987
7829021	62632169	8	~1986
7829051	15658103	8	~1985
7829219	15658439	8	~1985
7829351	15658703	8	~1985
7829573	46977439	8	~1986
7829593	46977559	8	~1986
7829603	15659207	8	~1985
7829617	46977703	8	~1986
7829917	46979503	8	~1986
7830157	46980943	8	~1986
7830271	125284337	9	~1987
7830371	62642969	8	~1986
7830457	46982743	8	~1986
7830503	15661007	8	~1985
7830611	15661223	8	~1985
7830671	15661343	8	~1985
7830731	15661463	8	~1985
7830973	46985839	8	~1986
7831079	15662159	8	~1985
7831163	579506063	9	~1989
7831283	15662567	8	~1985
7831301	62650409	8	~1986
7831337	62650697	8	~1986

Exp.	Prime Factor	Digits	Year
7831379	62651033	8	~1986
7831387	125302193	9	~1987
7831517	438564953	9	~1988
7831559	15663119	8	~1985
7831567	125305073	9	~1987
7832249	62657993	8	~1986
7832387	62659097	8	~1986
7832939	15665879	8	~1985
7832999	15665999	8	~1985
7833269	109665767	9	~1987
7833827	62670617	8	~1986
7833851	15667703	8	~1985
7834111	78341111	8	~1987
7834279	78342791	8	~1987
7834313	47005879	8	~1986
7834429	188026297	9	~1987
7834903	78349031	8	~1987
7835021	62680169	8	~1986
7835741	47014447	8	~1986
7836259	78362591	8	~1987
7836299	15672599	8	~1985
7836971	15673943	8	~1985
7837091	62696729	8	~1986
7837517	47025103	8	~1986
7837883	15675767	8	~1985

Exp.	Prime Factor	Digits	Year
7837981	47027887	8	~1986
7838321	62706569	8	~1986
7838687	141096367	9	~1987
7838879	15677759	8	~1985
7838893	47033359	8	~1986
7839017	62712137	8	~1986
7839121	47034727	8	~1986
7839131	15678263	8	~1985
7839137	62713097	8	~1986
7839199	78391991	8	~1987
7839263	15678527	8	~1985
7839479	15678959	8	~1985
7839493	47036959	8	~1986
7839511	141111199	9	~1987
7839641	47037847	8	~1986
7839719	15679439	8	~1985
7839911	62719289	8	~1986
7840271	15680543	8	~1985
7840439	15680879	8	~1985
7840523	15681047	8	~1985
7840691	15681383	8	~1985
7841219	62729753	8	~1986
7841677	125466833	9	~1987
7841759	62734073	8	~1986
7842031	125472497	9	~1987

Exp.	Prime Factor	Digits	Year
7842119	15684239	8	~1985
7842533	47055199	8	~1986
7842713	47056279	8	~1986
7843271	15686543	8	~1985
7843331	15686663	8	~1985
7843343	15686687	8	~1985
7843439	62747513	8	~1986
7843609	172559399	9	~1987
7843657	47061943	8	~1986
7843679	15687359	8	~1985
7843679	188248297	9
7843691	203935967	9	~1988
7843763	15687527	8	~1985
7843799	15687599	8	~1985
7843861	47063167	8	~1986
7844183	15688367	8	~1985
7844393	47066359	8	~1986
7844671	141204079	9	~1987
7844833	47068999	8	~1986
7844849	62758793	8	~1986
7844957	109829399	9	~1987
7845011	15690023	8	~1985
7845059	15690119	8	~1985
7845137	47070823	8	~1986
7845269	62762153	8	~1986

5.307.017 digits

26-01-11