Small Mersenne Prime Factors (page 964/5745)

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
8435579	16871159	8	~1985
8435579	202453897	9
8435711	16871423	8	~1985
8435743	84357431	8	~1987
8435831	16871663	8	~1985
8435939	16871879	8	~1985
8436023	16872047	8	~1985
8436353	50618119	8	~1986
8436499	84364991	8	~1987
8436599	67492793	8	~1987
8436671	16873343	8	~1985
8436671	607440313	9
8436809	67494473	8	~1987
8436977	67495817	8	~1987
8437181	67497449	8	~1987
8437211	16874423	8	~1985
8437433	50624599	8	~1986
8437727	67501817	8	~1987
8437733	50626399	8	~1986
8437861	50627167	8	~1986
8437931	16875863	8	~1985
8438141	50628847	8	~1986
8438351	16876703	8	~1985
8438377	50630263	8	~1986
8438399	16876799	8	~1985

Exp.	Prime Factor	Digits	Year
8438407	84384071	8	~1987
8438459	16876919	8	~1985
8438483	16876967	8	~1985
8438657	67509257	8	~1987
8438761	50632567	8	~1986
8439251	16878503	8	~1985
8439443	16878887	8	~1985
8439479	16878959	8	~1985
8439503	16879007	8	~1985
8439581	50637487	8	~1986
8439601	50637607	8	~1986
8440193	50641159	8	~1986
8440343	16880687	8	~1985
8440391	16880783	8	~1985
8440511	16881023	8	~1985
8440979	16881959	8	~1985
8441057	67528457	8	~1987
8441087	422054351	9	~1989
8441369	202592857	9	~1988
8441423	16882847	8	~1985
8441539	84415391	8	~1987
8441737	50650423	8	~1986
8441831	16883663	8	~1985
8442029	67536233	8	~1987
8442271	84422711	8	~1987

Exp.	Prime Factor	Digits	Year
8442359	67538873	8	~1987
8442437	67539497	8	~1987
8442767	675421361	9	~1989
8442779	16885559	8	~1985
8442781	50656687	8	~1986
8443079	16886159	8	~1985
8443117	50658703	8	~1986
8443199	67545593	8	~1987
8443361	50660167	8	~1986
8443453	50660719	8	~1986
8443651	151985719	9	~1987
8443709	270198689	9	~1988
8443913	50663479	8	~1986
8444003	16888007	8	~1985
8444123	16888247	8	~1985
8444363	16888727	8	~1985
8444573	50667439	8	~1986
8444591	16889183	8	~1985
8444957	118229399	9	~1987
8445523	135128369	9	~1987
8445601	337824041	9	~1988
8445683	16891367	8	~1985
8445707	67565657	8	~1987
8445961	50675767	8	~1986
8446019	16892039	8	~1985

Exp.	Prime Factor	Digits	Year
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
8449409	67595273	8	~1987
8449439	16898879	8	~1985

5.441.361 digits

26-03-15