Small Mersenne Prime Factors (page 409/5775)

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
2106421	46341263	8	~1983
2106431	4212863	7	~1980
2106437	29490119	8	~1982
2106479	16851833	8	~1982
2106491	4212983	7	~1980
2106551	4213103	7	~1980
2106737	80056007	8	~1984
2106781	12640687	8	~1982
2106781	33708497	8
2106781	46349183	8
2106877	12641263	8	~1982
2106877	556215529	9
2106931	391889167	9	~1985
2106983	1757223823	10	~1987
2107103	4214207	7	~1980
2107177	63215311	8	~1983
2107403	4214807	7	~1980
2107451	118017257	9	~1984
2107663	21076631	8	~1982
2107751	4215503	7	~1980
2107837	12647023	8	~1982
2107849	101176753	9	~1984
2108003	4216007	7	~1980
2108033	67457057	8	~1983
2108047	50593129	8	~1983

Exp.	Prime Factor	Digits	Year
2108063	4216127	7	~1980
2108177	269846657	9	~1985
2108263	21082631	8	~1982
2108453	63253591	8	~1983
2108497	33735953	8	~1983
2108531	4217063	7	~1980
2108669	16869353	8	~1982
2108809	50611417	8	~1983
2108839	84353561	8	~1984
2108879	16871033	8	~1982
2109053	29526743	8	~1982
2109179	4218359	7	~1980
2109179	16873433	8
2109253	113899663	9	~1984
2109311	4218623	7	~1980
2109403	33750449	8	~1983
2109553	12657319	8	~1982
2109617	29534639	8	~1982
2109619	1316402257	10	~1986
2109739	37975303	8	~1983
2109743	4219487	7	~1980
2109791	4219583	7	~1980
2109869	63296071	8	~1983
2109911	4219823	7	~1980
2109973	63299191	8	~1983

Exp.	Prime Factor	Digits	Year
2110019	4220039	7	~1980
2110037	29540519	8	~1982
2110063	21100631	8	~1982
2110103	4220207	7	~1980
2110259	4220519	7	~1980
2110343	4220687	7	~1980
2110439	37987903	8	~1983
2110469	29546567	8	~1982
2110523	4221047	7	~1980
2110543	21105431	8	~1982
2110553	12663319	8	~1982
2110621	63318631	8	~1983
2111051	16888409	8	~1982
2111159	4222319	7	~1980
2111177	12667063	8	~1982
2111231	16889849	8	~1982
2111303	253356361	9	~1985
2111311	21113111	8	~1982
2111311	38003599	8
2111357	29558999	8	~1982
2111387	16891097	8	~1982
2111453	29560343	8	~1982
2111491	21114911	8	~1982
2111497	12668983	8	~1982
2111513	12669079	8	~1982

Exp.	Prime Factor	Digits	Year
2111579	50677897	8	~1983
2111771	4223543	7	~1980
2111789	67577249	8	~1983
2111789	164719543	9
2111897	12671383	8	~1982
2111897	50685529	8
2112017	202753633	9	~1985
2112161	12672967	8	~1982
2112191	4224383	7	~1980
2112329	16898633	8	~1982
2112337	12674023	8	~1982
2112353	50696473	8	~1983
2112353	168988241	9
2112419	4224839	7	~1980
2112569	16900553	8	~1982
2112713	67606817	8	~1983
2112827	16902617	8	~1982
2112827	50707849	8
2112841	46482503	8	~1983
2112953	12677719	8	~1982
2113037	12678223	8	~1982
2113211	4226423	7	~1980
2113451	4226903	7	~1980
2113471	38042479	8	~1983
2113511	4227023	7	~1980

5.471.290 digits

26-03-29