Small Mersenne Prime Factors (page 953/5025)

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
8986391	17972783	8	~1985
8986751	17973503	8	~1985
8986801	53920807	8	~1986
8986841	53921047	8	~1986
8986933	53921599	8	~1986
8986987	359479481	9	~1988
8987197	53923183	8	~1986
8987243	17974487	8	~1985
8987449	197723879	9	~1988
8987449	431397553	9
8987519	17975039	8	~1985
8987567	71900537	8	~1987
8987591	17975183	8	~1985
8987621	53925727	8	~1986
8988131	17976263	8	~1985
8988191	17976383	8	~1985
8988437	53930623	8	~1986
8988437	71907497	8
8988557	71908457	8	~1987
8988613	53931679	8	~1986
8988839	17977679	8	~1985
8988877	53933263	8	~1986
8988989	71911913	8	~1987
8989199	71913593	8	~1987
8989237	53935423	8	~1986

Exp.	Prime Factor	Digits	Year
8989499	17978999	8	~1985
8989621	53937727	8	~1986
8989691	161814439	9	~1988
8989763	17979527	8	~1985
8990153	53940919	8	~1986
8990257	53941543	8	~1986
8990563	89905631	8	~1987
8990777	53944663	8	~1986
8990843	17981687	8	~1985
8991197	53947183	8	~1986
8991239	17982479	8	~1985
8991347	449567351	9	~1989
8991371	17982743	8	~1985
8991743	17983487	8	~1985
8991901	53951407	8	~1986
8992019	17984039	8	~1985
8992259	161860663	9	~1988
8992283	17984567	8	~1985
8992499	17984999	8	~1985
8992769	71942153	8	~1987
8992811	17985623	8	~1985
8992937	53957623	8	~1986
8993011	89930111	8	~1987
8993297	53959783	8	~1986
8993333	53959999	8	~1986

Exp.	Prime Factor	Digits	Year
8993447	109666092719	12	~1995
8993723	17987447	8	~1985
8993737	53962423	8	~1986
8993861	71950889	8	~1987
8993951	17987903	8	~1985
8994473	53966839	8	~1986
8994593	125924303	9	~1987
8994659	17989319	8	~1985
8994677	125925479	9	~1987
8994911	17989823	8	~1985
8995109	71960873	8	~1987
8995163	17990327	8	~1985
8995391	17990783	8	~1985
8995583	17991167	8	~1985
8995751	17991503	8	~1985
8995799	17991599	8	~1985
8995801	53974807	8	~1986
8995837	53975023	8	~1986
8995957	143935313	9	~1987
8996539	89965391	8	~1987
8996579	17993159	8	~1985
8996639	17993279	8	~1985
8996651	431839249	9	~1989
8996831	17993663	8	~1985
8997011	17994023	8	~1985

Exp.	Prime Factor	Digits	Year
8997239	17994479	8	~1985
8997311	17994623	8	~1985
8997503	17995007	8	~1985
8997871	89978711	8	~1987
8998271	17996543	8	~1985
8998307	71986457	8	~1987
8998651	161975719	9	~1988
8998883	17997767	8	~1985
8998919	17997839	8	~1985
8999051	17998103	8	~1985
8999183	17998367	8	~1985
8999423	17998847	8	~1985
9000203	18000407	8	~1985
9000577	54003463	8	~1986
9000637	54003823	8	~1986
9000683	18001367	8	~1985
9000709	198015599	9	~1988
9000721	144011537	9	~1987
9001163	810104671	9	~1989
9001337	54008023	8	~1986
9001511	18003023	8	~1985
9001799	18003599	8	~1985
9001933	54011599	8	~1986
9002249	72017993	8	~1987
9002849	72022793	8	~1987

4.724.182 digits

25-04-13