Small Mersenne Prime Factors (page 749/5190)

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
5815721	46525769	8	~1985
5815811	11631623	8	~1984
5816243	11632487	8	~1984
5816339	11632679	8	~1984
5816387	46531097	8	~1985
5816453	34898719	8	~1985
5816549	46532393	8	~1985
5816611	232664441	9	~1987
5816971	58169711	8	~1986
5817061	34902367	8	~1985
5817061	127975343	9
5817347	46538777	8	~1985
5817541	511943609	9	~1988
5817653	34905919	8	~1985
5817907	58179071	8	~1986
5818073	34908439	8	~1985
5818277	34909663	8	~1985
5818283	11636567	8	~1984
5818391	11636783	8	~1984
5818493	34910959	8	~1985
5818619	11637239	8	~1984
5818819	58188191	8	~1986
5818853	558609889	9	~1988
5819189	314236207	9	~1987
5819279	11638559	8	~1984

Exp.	Prime Factor	Digits	Year
5819293	34915759	8	~1985
5819543	11639087	8	~1984
5819557	34917343	8	~1985
5819647	232785881	9	~1987
5819773	93116369	8	~1986
5820041	46560329	8	~1985
5820233	34921399	8	~1985
5820421	34922527	8	~1985
5820481	34922887	8	~1985
5820583	58205831	8	~1986
5820623	11641247	8	~1984
5820673	93130769	8	~1986
5820959	11641919	8	~1984
5820977	46567817	8	~1985
5821019	11642039	8	~1984
5821037	34926223	8	~1985
5821229	46569833	8	~1985
5821289	46570313	8	~1985
5821853	34931119	8	~1985
5821919	11643839	8	~1984
5821979	46575833	8	~1985
5822111	11644223	8	~1984
5822137	34932823	8	~1985
5822147	46577177	8	~1985
5822471	46579769	8	~1985

Exp.	Prime Factor	Digits	Year
5822567	46580537	8	~1985
5823019	58230191	8	~1986
5823149	46585193	8	~1985
5823239	279515473	9	~1987
5823341	34940047	8	~1985
5823563	11647127	8	~1984
5823659	11647319	8	~1984
5823869	46590953	8	~1985
5824211	11648423	8	~1984
5824277	34945663	8	~1985
5824417	34946503	8	~1985
5824499	570800903	9	~1988
5824631	11649263	8	~1984
5824649	46597193	8	~1985
5824739	11649479	8	~1984
5824789	1630940921	10	~1989
5824813	128145887	9	~1986
5824979	11649959	8	~1984
5825297	46602377	8	~1985
5825431	58254311	8	~1986
5825591	46604729	8	~1985
5825653	93210449	8	~1986
5825843	11651687	8	~1984
5826133	34956799	8	~1985
5826259	58262591	8	~1986

Exp.	Prime Factor	Digits	Year
5826311	11652623	8	~1984
5826451	58264511	8	~1986
5826497	34958983	8	~1985
5826599	11653199	8	~1984
5827103	11654207	8	~1984
5827177	34963063	8	~1985
5827343	326331209	9	~1987
5827439	11654879	8	~1984
5827511	11655023	8	~1984
5827823	11655647	8	~1984
5828233	34969399	8	~1985
5828309	46626473	8	~1985
5828369	139880857	9	~1986
5828567	46628537	8	~1985
5828567	104914207	9
5828917	34973503	8	~1985
5828941	34973647	8	~1985
5829001	128238023	9	~1986
5829041	46632329	8	~1985
5829119	11658239	8	~1984
5829119	291455951	9
5829127	139899049	9	~1986
5829137	139899289	9	~1986
5829391	93270257	8	~1986
5829533	34977199	8	~1985

4.888.230 digits

25-06-29