Small Mersenne Prime Factors (page 934/5205)

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
8451517	50709103	8	~1986
8451851	16903703	8	~1985
8451893	50711359	8	~1986
8452019	16904039	8	~1985
8452097	50712583	8	~1986
8452141	50712847	8	~1986
8452307	67618457	8	~1987
8452403	16904807	8	~1985
8452439	16904879	8	~1985
8452441	50714647	8	~1986
8452571	16905143	8	~1985
8452681	50716087	8	~1986
8452721	50716327	8	~1986
8452877	118340279	9	~1987
8453099	16906199	8	~1985
8453177	67625417	8	~1987
8453597	67628777	8	~1987
8453639	16907279	8	~1985
8453663	16907327	8	~1985
8453693	50722159	8	~1986
8453759	16907519	8	~1985
8453821	50722927	8	~1986
8453849	67630793	8	~1987
8453897	50723383	8	~1986
8453909	118354727	9	~1987

Exp.	Prime Factor	Digits	Year
8453999	16907999	8	~1985
8454067	152173207	9	~1987
8454191	16908383	8	~1985
8454211	84542111	8	~1987
8454371	7524390191	10	~1992
8454623	16909247	8	~1985
8454739	152185303	9	~1987
8454923	16909847	8	~1985
8454947	67639577	8	~1987
8455091	16910183	8	~1985
8455151	16910303	8	~1985
8455259	67642073	8	~1987
8455301	67642409	8	~1987
8455561	50733367	8	~1986
8455597	50733583	8	~1986
8455633	50733799	8	~1986
8455691	152202439	9	~1987
8456039	16912079	8	~1985
8456213	50737279	8	~1986
8456221	405898609	9	~1988
8456419	84564191	8	~1987
8456467	84564671	8	~1987
8456543	16913087	8	~1985
8456753	50740519	8	~1986
8456753	473578169	9

Exp.	Prime Factor	Digits	Year
8456761	50740567	8	~1986
8456891	16913783	8	~1985
8457563	16915127	8	~1985
8457781	50746687	8	~1986
8457989	67663913	8	~1987
8458001	50748007	8	~1986
8458091	16916183	8	~1985
8458117	50748703	8	~1986
8458369	592085831	9	~1989
8458501	50751007	8	~1986
8458811	16917623	8	~1985
8458991	16917983	8	~1985
8459173	135346769	9	~1987
8459417	67675337	8	~1987
8459441	67675529	8	~1987
8459651	16919303	8	~1985
8459723	16919447	8	~1985
8459747	67677977	8	~1987
8459821	50758927	8	~1986
8459831	16919663	8	~1985
8460191	16920383	8	~1985
8460581	50763487	8	~1986
8461241	50767447	8	~1986
8461247	67689977	8	~1987
8461507	84615071	8	~1987

Exp.	Prime Factor	Digits	Year
8461549	186154079	9	~1988
8461643	16923287	8	~1985
8461757	50770543	8	~1986
8462081	50772487	8	~1986
8462477	50774863	8	~1986
8462579	16925159	8	~1985
8462819	16925639	8	~1985
8462819	67702553	8
8462879	16925759	8	~1985
8462903	16925807	8	~1985
8463193	50779159	8	~1986
8463353	473947769	9	~1989
8463979	84639791	8	~1987
8464331	67714649	8	~1987
8464517	50787103	8	~1986
8464811	16929623	8	~1985
8464837	50789023	8	~1986
8465623	287831183	9	~1988
8465713	50794279	8	~1986
8465819	16931639	8	~1985
8465927	67727417	8	~1987
8466043	84660431	8	~1987
8466043	355573807	9
8466079	84660791	8	~1987
8466443	16932887	8	~1985

4.903.097 digits

25-07-08