Small Mersenne Prime Factors (page 957/5610)

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
8445961	50675767	8	~1986
8446019	16892039	8	~1985
8446019	67568153	8
8446063	84460631	8	~1987
8446283	16892567	8	~1985
8446421	67571369	8	~1987
8446913	50681479	8	~1986
8446979	16893959	8	~1985
8447111	16894223	8	~1985
8447171	67577369	8	~1987
8447177	50683063	8	~1986
8447423	16894847	8	~1985
8447591	16895183	8	~1985
8447653	50685919	8	~1986
8447711	16895423	8	~1985
8448017	50688103	8	~1986
8448197	50689183	8	~1986
8448431	16896863	8	~1985
8448431	219659207	9
8448551	16897103	8	~1985
8448851	16897703	8	~1985
8449097	50694583	8	~1986
8449139	16898279	8	~1985
8449223	16898447	8	~1985
8449361	50696167	8	~1986

Exp.	Prime Factor	Digits	Year
8449409	67595273	8	~1987
8449439	16898879	8	~1985
8449513	50697079	8	~1986
8449711	84497111	8	~1987
8449979	16899959	8	~1985
8450069	118300967	9	~1987
8450291	67602329	8	~1987
8450423	16900847	8	~1985
8450483	16900967	8	~1985
8450881	50705287	8	~1986
8450947	84509471	8	~1987
8450969	67607753	8	~1987
8451041	50706247	8	~1986
8451271	84512711	8	~1987
8451491	16902983	8	~1985
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

Exp.	Prime Factor	Digits	Year
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
8453681	67629449	8	~1987
8453693	50722159	8	~1986
8453759	16907519	8	~1985
8453821	50722927	8	~1986
8453849	67630793	8	~1987
8453897	50723383	8	~1986
8453909	118354727	9	~1987
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

Exp.	Prime Factor	Digits	Year
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
8456561	67652489	8	~1987
8456753	50740519	8	~1986
8456753	473578169	9
8456761	50740567	8	~1986
8456891	16913783	8	~1985
8456927	67655417	8	~1987
8457107	67656857	8	~1987
8457563	16915127	8	~1985
8457599	67660793	8	~1987
8457781	50746687	8	~1986
8457989	67663913	8	~1987

5.307.017 digits

26-01-11