Small Mersenne Prime Factors (page 917/5340)

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
8075999	16151999	8	~1985
8076371	16152743	8	~1985
8076443	16152887	8	~1985
8076599	193838377	9	~1988
8076641	48459847	8	~1986
8076701	48460207	8	~1986
8076707	64613657	8	~1986
8076779	16153559	8	~1985
8076961	48461767	8	~1986
8076977	48461863	8	~1986
8076983	16153967	8	~1985
8077259	16154519	8	~1985
8077271	16154543	8	~1985
8077379	16154759	8	~1985
8077529	113085407	9	~1987
8077621	371570567	9	~1988
8077847	64622777	8	~1986
8077913	48467479	8	~1986
8077967	64623737	8	~1986
8078069	500840279	9	~1989
8078201	64625609	8	~1986
8078951	16157903	8	~1985
8079041	48474247	8	~1986
8079299	16158599	8	~1985
8079497	48476983	8	~1986

Exp.	Prime Factor	Digits	Year
8079779	145436023	9	~1987
8079857	64638857	8	~1986
8080201	48481207	8	~1986
8080201	630255679	9
8080223	16160447	8	~1985
8080229	64641833	8	~1986
8080283	16160567	8	~1985
8080313	48481879	8	~1986
8080343	16160687	8	~1985
8080451	64643609	8	~1986
8080651	80806511	8	~1987
8080679	16161359	8	~1985
8080693	48484159	8	~1986
8080931	64647449	8	~1986
8080957	48485743	8	~1986
8081041	48486247	8	~1986
8081057	48486343	8	~1986
8081093	888920231	9	~1989
8081221	177786863	9	~1987
8081351	16162703	8	~1985
8081399	16162799	8	~1985
8081471	16162943	8	~1985
8081501	307097039	9	~1988
8081527	80815271	8	~1987
8081543	16163087	8	~1985

Exp.	Prime Factor	Digits	Year
8081663	16163327	8	~1985
8082161	48492967	8	~1986
8082251	16164503	8	~1985
8082311	16164623	8	~1985
8082653	48495919	8	~1986
8083139	16166279	8	~1985
8083259	16166519	8	~1985
8083391	16166783	8	~1985
8083643	16167287	8	~1985
8084099	16168199	8	~1985
8084159	16168319	8	~1985
8084647	80846471	8	~1987
8085437	64683497	8	~1986
8085449	194050777	9	~1988
8085503	16171007	8	~1985
8085793	48514759	8	~1986
8085911	64687289	8	~1986
8086139	64689113	8	~1986
8086277	64690217	8	~1986
8086321	48517927	8	~1986
8086657	48519943	8	~1986
8086697	48520183	8	~1986
8086843	129389489	9	~1987
8086931	16173863	8	~1985
8087153	48522919	8	~1986

Exp.	Prime Factor	Digits	Year
8087333	48523999	8	~1986
8087371	1099882457	10	~1989
8087477	48524863	8	~1986
8087591	64700729	8	~1986
8087591	210277367	9
8087707	533788663	9	~1989
8087813	48526879	8	~1986
8087861	64702889	8	~1986
8087951	16175903	8	~1985
8088323	16176647	8	~1985
8088389	64707113	8	~1986
8088467	64707737	8	~1986
8088761	64710089	8	~1986
8089049	64712393	8	~1986
8089391	16178783	8	~1985
8089619	16179239	8	~1985
8089799	16179599	8	~1985
8090041	3478717631	10	~1991
8090141	48540847	8	~1986
8090267	64722137	8	~1986
8090279	16180559	8	~1985
8090651	16181303	8	~1985
8090711	16181423	8	~1985
8090843	16181687	8	~1985
8090993	113273903	9	~1987

5.037.460 digits

25-09-07