Small Mersenne Prime Factors (page 668/5610)

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
4607423	9214847	7	~1983
4607467	46074671	8	~1985
4607591	36860729	8	~1985
4607653	101368367	9	~1986
4607819	9215639	7	~1983
4607857	73725713	8	~1985
4607957	36863657	8	~1985
4608631	46086311	8	~1985
4608881	27653287	8	~1984
4608917	27653503	8	~1984
4609079	82963423	8	~1985
4609093	27654559	8	~1984
4609259	9218519	7	~1983
4609271	9218543	7	~1983
4609271	36874169	8
4609313	138279391	9	~1986
4609393	27656359	8	~1984
4609481	27656887	8	~1984
4610057	396464903	9	~1987
4610387	36883097	8	~1985
4610393	27662359	8	~1984
4610453	64546343	8	~1985
4610693	27664159	8	~1984
4610759	9221519	7	~1983
4610783	9221567	7	~1983

Exp.	Prime Factor	Digits	Year
4610789	110658937	9	~1986
4610821	101438063	9	~1986
4610843	9221687	7	~1983
4610897	36887177	8	~1985
4610999	9221999	7	~1983
4611209	36889673	8	~1985
4611391	73782257	8	~1985
4611443	9222887	7	~1983
4611457	27668743	8	~1984
4611613	27669679	8	~1984
4611697	27670183	8	~1984
4611779	9223559	7	~1983
4611923	9223847	7	~1983
4612001	36896009	8	~1985
4612187	83019367	8	~1985
4612199	9224399	7	~1983
4612217	36897737	8	~1985
4612313	64572383	8	~1985
4612343	9224687	7	~1983
4612477	27674863	8	~1984
4612477	73799633	8
4612511	9225023	7	~1983
4612571	9225143	7	~1983
4612571	36900569	8
4612669	110704057	9	~1986

Exp.	Prime Factor	Digits	Year
4612709	64577927	8	~1985
4612859	9225719	7	~1983
4612987	2657080513	10	~1989
4613051	36904409	8	~1985
4613071	73809137	8	~1985
4613237	27679423	8	~1984
4613701	73819217	8	~1985
4614173	27685039	8	~1984
4614347	258403433	9	~1987
4614349	221488753	9	~1986
4614419	36915353	8	~1985
4614479	9228959	7	~1983
4614713	27688279	8	~1984
4614719	9229439	7	~1983
4614839	9229679	7	~1983
4614901	406111289	9	~1987
4614971	9229943	7	~1983
4614983	9229967	7	~1983
4614997	138449911	9	~1986
4615057	73840913	8	~1985
4615073	110761753	9	~1986
4615099	46150991	8	~1985
4615333	27691999	8	~1984
4615603	156930503	9	~1986
4615991	9231983	7	~1983

Exp.	Prime Factor	Digits	Year
4615991	36927929	8
4615999	46159991	8	~1985
4616033	27696199	8	~1984
4616063	9232127	7	~1983
4616113	27696679	8	~1984
4616317	27697903	8	~1984
4616347	46163471	8	~1985
4616413	27698479	8	~1984
4616497	73863953	8	~1985
4616531	36932249	8	~1985
4616587	46165871	8	~1985
4616603	9233207	7	~1983
4616879	9233759	7	~1983
4617073	73873169	8	~1985
4617143	9234287	7	~1983
4617161	36937289	8	~1985
4617199	221625553	9	~1986
4617479	9234959	7	~1983
4617493	27704959	8	~1984
4617533	27705199	8	~1984
4617541	27705247	8	~1984
4617617	27705703	8	~1984
4617737	27706423	8	~1984
4617737	36941897	8
4618001	27708007	8	~1984

5.307.017 digits

26-01-11