Small Mersenne Prime Factors (page 942/5550)

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
8275213	331008521	9	~1988
8275343	16550687	8	~1985
8275381	49652287	8	~1986
8275391	66203129	8	~1986
8275439	16550879	8	~1985
8275439	198610537	9
8275451	16550903	8	~1985
8275601	49653607	8	~1986
8276063	215177639	9	~1988
8276201	66209609	8	~1986
8276351	16552703	8	~1985
8276591	16553183	8	~1985
8276693	49660159	8	~1986
8276693	1853979233	10
8276713	49660279	8	~1986
8276797	49660783	8	~1986
8277221	66217769	8	~1986
8277323	16554647	8	~1985
8277617	49665703	8	~1986
8277617	66220937	8
8277653	49665919	8	~1986
8277697	132443153	9	~1987
8277707	463551593	9	~1989
8277719	16555439	8	~1985
8278013	49668079	8	~1986

Exp.	Prime Factor	Digits	Year
8278037	66224297	8	~1986
8278073	49668439	8	~1986
8278097	49668583	8	~1986
8278297	49669783	8	~1986
8278301	66226409	8	~1986
8278559	16557119	8	~1985
8278619	16557239	8	~1985
8278681	132458897	9	~1987
8278799	66230393	8	~1986
8278943	16557887	8	~1985
8279023	82790231	8	~1987
8279423	16558847	8	~1985
8279549	66236393	8	~1986
8279633	115914863	9	~1987
8279651	16559303	8	~1985
8279699	16559399	8	~1985
8279729	66237833	8	~1986
8279963	16559927	8	~1985
8280263	16560527	8	~1985
8280491	16560983	8	~1985
8280761	49684567	8	~1986
8280791	66246329	8	~1987
8280911	16561823	8	~1985
8281313	49687879	8	~1986
8281379	16562759	8	~1985

Exp.	Prime Factor	Digits	Year
8281571	16563143	8	~1985
8281579	82815791	8	~1987
8282003	16564007	8	~1985
8282063	16564127	8	~1985
8282129	66257033	8	~1987
8282159	16564319	8	~1985
8282189	115950647	9	~1987
8282291	66258329	8	~1987
8282411	149083399	9	~1987
8282453	115954343	9	~1987
8282633	49695799	8	~1986
8282759	16565519	8	~1985
8283001	49698007	8	~1986
8283257	49699543	8	~1986
8283263	16566527	8	~1985
8283503	16567007	8	~1985
8283547	82835471	8	~1987
8283923	16567847	8	~1985
8284033	49704199	8	~1986
8284103	16568207	8	~1985
8284127	66273017	8	~1987
8284373	198824953	9	~1988
8284447	82844471	8	~1987
8284739	16569479	8	~1985
8284823	16569647	8	~1985

Exp.	Prime Factor	Digits	Year
8284823	198835753	9
8284841	49709047	8	~1986
8284949	66279593	8	~1987
8285411	16570823	8	~1985
8285591	16571183	8	~1985
8285621	66284969	8	~1987
8285639	66285113	8	~1987
8285831	16571663	8	~1985
8286203	16572407	8	~1985
8286209	66289673	8	~1987
8286253	49717519	8	~1986
8286569	513767279	9	~1989
8286671	16573343	8	~1985
8286683	16573367	8	~1985
8286731	16573463	8	~1985
8287271	16574543	8	~1985
8287717	132603473	9	~1987
8287817	49726903	8	~1986
8287871	66302969	8	~1987
8288057	66304457	8	~1987
8288081	314947079	9	~1988
8288183	16576367	8	~1985
8288353	49730119	8	~1986
8288459	16576919	8	~1985
8288543	16577087	8	~1985

5.247.179 digits

25-12-14