Small Mersenne Prime Factors (page 595/5445)

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
3877589	31020713	8	~1984
3877631	7755263	7	~1982
3877813	23266879	8	~1984
3878177	31025417	8	~1984
3878183	7756367	7	~1982
3878279	7756559	7	~1982
3878519	93084457	8	~1985
3878753	54302543	8	~1985
3878759	31030073	8	~1984
3878981	31031849	8	~1984
3878993	54305903	8	~1985
3879199	131892767	9	~1985
3879311	124137953	9	~1985
3879361	23276167	8	~1984
3879517	93108409	8	~1985
3879671	7759343	7	~1982
3879719	7759439	7	~1982
3879721	23278327	8	~1984
3879839	31038713	8	~1984
3880033	23280199	8	~1984
3880091	7760183	7	~1982
3880241	31041929	8	~1984
3880381	745033153	9	~1987
3880447	62087153	8	~1985
3880601	31044809	8	~1984

Exp.	Prime Factor	Digits	Year
3880733	23284399	8	~1984
3880817	31046537	8	~1984
3880927	62094833	8	~1985
3881021	31048169	8	~1984
3881027	100906703	9	~1985
3881077	23286463	8	~1984
3881161	62098577	8	~1985
3881173	23287039	8	~1984
3881299	69863383	8	~1985
3881303	7762607	7	~1982
3881431	69865759	8	~1985
3882353	54352943	8	~1985
3882421	23294527	8	~1984
3882569	31060553	8	~1984
3882911	31063289	8	~1984
3882911	69892399	8
3882947	100956623	9	~1985
3883073	23298439	8	~1984
3883133	23298799	8	~1984
3883177	23299063	8	~1984
3883541	23301247	8	~1984
3883547	93205129	8	~1985
3883597	23301583	8	~1984
3883823	7767647	7	~1982
3884117	23304703	8	~1984

Exp.	Prime Factor	Digits	Year
3884123	7768247	7	~1982
3884213	3286044199	10	~1989
3884261	23305567	8	~1984
3884267	652556857	9	~1987
3884333	116529991	9	~1985
3884473	62151569	8	~1985
3884533	23307199	8	~1984
3884731	69925159	8	~1985
3884767	38847671	8	~1984
3884819	7769639	7	~1982
3885103	38851031	8	~1984
3885181	23311087	8	~1984
3885461	23312767	8	~1984
3885521	31084169	8	~1984
3885697	23314183	8	~1984
3885743	7771487	7	~1982
3885779	7771559	7	~1982
3885989	54403847	8	~1985
3886117	23316703	8	~1984
3886199	7772399	7	~1982
3886229	54407207	8	~1985
3886231	38862311	8	~1984
3886357	23318143	8	~1984
3886537	62184593	8	~1985
3886559	7773119	7	~1982

Exp.	Prime Factor	Digits	Year
3886637	23319823	8	~1984
3886717	62187473	8	~1985
3886723	62187569	8	~1985
3886801	23320807	8	~1984
3886937	31095497	8	~1984
3886991	31095929	8	~1984
3887003	7774007	7	~1982
3887171	7774343	7	~1982
3887291	31098329	8	~1984
3887357	31098857	8	~1984
3887393	23324359	8	~1984
3887399	7774799	7	~1982
3887489	54424847	8	~1985
3887519	7775039	7	~1982
3887519	69975343	8
3887581	23325487	8	~1984
3887771	7775543	7	~1982
3887771	69979879	8
3887839	38878391	8	~1984
3887893	155515721	9	~1986
3887993	23327959	8	~1984
3888463	38884631	8	~1984
3888551	7777103	7	~1982
3888611	7777223	7	~1982
3888629	54440807	8	~1985

5.142.307 digits

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