Small Mersenne Prime Factors (page 910/5025)

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
8265431	16530863	8	~1985
8265539	16531079	8	~1985
8265833	49594999	8	~1986
8265919	82659191	8	~1987
8265973	132255569	9	~1987
8265979	82659791	8	~1987
8266129	181854839	9	~1988
8266373	115729223	9	~1987
8266513	49599079	8	~1986
8266931	16533863	8	~1985
8267339	66138713	8	~1986
8267351	16534703	8	~1985
8267951	16535903	8	~1985
8268241	49609447	8	~1986
8268497	49610983	8	~1986
8268803	16537607	8	~1985
8268893	115764503	9	~1987
8268899	66151193	8	~1986
8268913	49613479	8	~1986
8269013	49614079	8	~1986
8269043	16538087	8	~1985
8269439	66155513	8	~1986
8269559	16539119	8	~1985
8269619	16539239	8	~1985
8269711	132315377	9	~1987

Exp.	Prime Factor	Digits	Year
8269763	16539527	8	~1985
8270033	49620199	8	~1986
8270039	198480937	9	~1988
8270201	49621207	8	~1986
8270671	148872079	9	~1987
8270711	16541423	8	~1985
8270881	49625287	8	~1986
8271049	181963079	9	~1988
8271521	49629127	8	~1986
8271839	16543679	8	~1985
8271841	49631047	8	~1986
8272097	115809359	9	~1987
8272177	49633063	8	~1986
8272403	16544807	8	~1985
8272483	132359729	9	~1987
8272681	49636087	8	~1986
8272763	16545527	8	~1985
8272787	215092463	9	~1988
8272861	248185831	9	~1988
8273453	49640719	8	~1986
8273579	16547159	8	~1985
8273773	49642639	8	~1986
8273879	16547759	8	~1985
8274023	16548047	8	~1985
8274137	66193097	8	~1986

Exp.	Prime Factor	Digits	Year
8274239	16548479	8	~1985
8274547	1125338393	10	~1989
8274559	82745591	8	~1987
8274677	49648063	8	~1986
8274901	49649407	8	~1986
8275133	198603193	9	~1988
8275213	331008521	9	~1988
8275343	16550687	8	~1985
8275381	49652287	8	~1986
8275439	16550879	8	~1985
8275439	198610537	9
8275451	16550903	8	~1985
8275601	49653607	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
8277323	16554647	8	~1985
8277617	49665703	8	~1986
8277653	49665919	8	~1986
8277697	132443153	9	~1987
8277707	463551593	9	~1989
8277719	16555439	8	~1985

Exp.	Prime Factor	Digits	Year
8278013	49668079	8	~1986
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
8278943	16557887	8	~1985
8279023	82790231	8	~1987
8279423	16558847	8	~1985
8279651	16559303	8	~1985
8279699	16559399	8	~1985
8279963	16559927	8	~1985
8280263	16560527	8	~1985
8280491	16560983	8	~1985
8280761	49684567	8	~1986
8280911	16561823	8	~1985
8281313	49687879	8	~1986
8281379	16562759	8	~1985
8281571	16563143	8	~1985
8281579	82815791	8	~1987
8282003	16564007	8	~1985
8282063	16564127	8	~1985

4.724.182 digits

25-04-13