Small Mersenne Prime Factors (page 966/5490)

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
8680157	52080943	8	~1986
8680229	69441833	8	~1987
8680313	52081879	8	~1986
8680391	277772513	9	~1988
8680481	69443849	8	~1987
8680583	17361167	8	~1985
8680697	52084183	8	~1986
8680733	52084399	8	~1986
8680811	17361623	8	~1985
8680823	17361647	8	~1985
8681177	69449417	8	~1987
8681489	69451913	8	~1987
8682143	364650007	9	~1988
8682199	86821991	8	~1987
8682659	17365319	8	~1985
8682851	17365703	8	~1985
8683097	69464777	8	~1987
8683237	607826591	9	~1989
8683331	17366663	8	~1985
8683427	69467417	8	~1987
8683439	17366879	8	~1985
8683517	52101103	8	~1986
8683637	52101823	8	~1986
8683639	625222009	9	~1989
8684099	17368199	8	~1985

Exp.	Prime Factor	Digits	Year
8684213	52105279	8	~1986
8684437	52106623	8	~1986
8684521	52107127	8	~1986
8684657	52107943	8	~1986
8684693	52108159	8	~1986
8684699	17369399	8	~1985
8684759	17369519	8	~1985
8684771	17369543	8	~1985
8685073	191071607	9	~1988
8685167	69481337	8	~1987
8685263	17370527	8	~1985
8685667	138970673	9	~1987
8685791	17371583	8	~1985
8685863	17371727	8	~1985
8685923	17371847	8	~1985
8686259	17372519	8	~1985
8686679	17373359	8	~1985
8687093	52122559	8	~1986
8687183	17374367	8	~1985
8687233	52123399	8	~1986
8687797	52126783	8	~1986
8687891	17375783	8	~1985
8688059	17376119	8	~1985
8688083	17376167	8	~1985
8688287	225895463	9	~1988

Exp.	Prime Factor	Digits	Year
8688299	17376599	8	~1985
8688353	52130119	8	~1986
8688551	17377103	8	~1985
8688611	17377223	8	~1985
8688613	191149487	9	~1988
8688809	69510473	8	~1987
8689259	17378519	8	~1985
8689433	52136599	8	~1986
8689451	17378903	8	~1985
8689463	17378927	8	~1985
8689529	69516233	8	~1987
8689661	69517289	8	~1987
8689979	17379959	8	~1985
8690093	52140559	8	~1986
8690303	17380607	8	~1985
8690399	17380799	8	~1985
8690797	52144783	8	~1986
8691167	990793039	9	~1989
8691239	17382479	8	~1985
8691383	17382767	8	~1985
8691731	17383463	8	~1985
8691901	139070417	9	~1987
8692223	17384447	8	~1985
8692331	69538649	8	~1987
8692417	52154503	8	~1986

Exp.	Prime Factor	Digits	Year
8692417	139078673	9
8692961	260788831	9	~1988
8693263	86932631	8	~1987
8693687	69549497	8	~1987
8694551	17389103	8	~1985
8694683	17389367	8	~1985
8694739	86947391	8	~1987
8694767	156505807	9	~1988
8695061	52170367	8	~1986
8695069	608654831	9	~1989
8695079	17390159	8	~1985
8695207	86952071	8	~1987
8695213	52171279	8	~1986
8695343	17390687	8	~1985
8695543	86955431	8	~1987
8695601	69564809	8	~1987
8695663	86956631	8	~1987
8695859	17391719	8	~1985
8696063	17392127	8	~1985
8696161	52176967	8	~1986
8696321	52177927	8	~1986
8696321	69570569	8
8696561	52179367	8	~1986
8696617	52179703	8	~1986
8696711	17393423	8	~1985

5.187.277 digits

25-11-17