Small Mersenne Prime Factors (page 740/5340)

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
5612951	44903609	8	~1985
5613217	89811473	8	~1986
5613431	11226863	8	~1984
5613457	33680743	8	~1985
5613563	11227127	8	~1984
5613623	11227247	8	~1984
5613857	44910857	8	~1985
5614061	33684367	8	~1985
5614223	11228447	8	~1984
5614523	11229047	8	~1984
5614589	44916713	8	~1985
5614681	33688087	8	~1985
5614919	44919353	8	~1985
5615107	56151071	8	~1985
5615167	89842673	8	~1986
5615213	33691279	8	~1985
5615273	33691639	8	~1985
5615579	11231159	8	~1984
5615699	11231399	8	~1984
5615713	33694279	8	~1985
5615723	11231447	8	~1984
5615741	33694447	8	~1985
5615803	56158031	8	~1985
5615891	11231783	8	~1984
5616097	89857553	8	~1986

Exp.	Prime Factor	Digits	Year
5616277	33697663	8	~1985
5616383	134793193	9	~1986
5616389	168491671	9	~1987
5616431	11232863	8	~1984
5616431	235890103	9
5616433	168492991	9	~1987
5616557	269594737	9	~1987
5616643	56166431	8	~1985
5616679	1179502591	10	~1989
5616883	56168831	8	~1985
5616893	33701359	8	~1985
5616967	56169671	8	~1985
5617043	11234087	8	~1984
5617211	11234423	8	~1984
5617301	33703807	8	~1985
5617349	44938793	8	~1985
5617421	33704527	8	~1985
5617421	44939369	8
5617499	11234999	8	~1984
5617639	5347992329	10	~1990
5617741	33706447	8	~1985
5617897	89886353	8	~1986
5618027	101124487	9	~1986
5618111	11236223	8	~1984
5618441	33710647	8	~1985

Exp.	Prime Factor	Digits	Year
5618579	44948633	8	~1985
5618581	33711487	8	~1985
5618777	33712663	8	~1985
5619143	11238287	8	~1984
5619203	11238407	8	~1984
5619379	56193791	8	~1985
5619473	78672623	8	~1986
5619487	56194871	8	~1985
5619547	56195471	8	~1985
5619683	11239367	8	~1984
5619701	44957609	8	~1985
5619919	56199191	8	~1985
5619983	11239967	8	~1984
5620091	11240183	8	~1984
5620271	11240543	8	~1984
5620339	629477969	9	~1988
5620451	11240903	8	~1984
5620453	33722719	8	~1985
5620493	33722959	8	~1985
5620709	44965673	8	~1985
5620799	44966393	8	~1985
5620913	33725479	8	~1985
5621437	33728623	8	~1985
5621471	44971769	8	~1985
5621687	44973497	8	~1985

Exp.	Prime Factor	Digits	Year
5621753	33730519	8	~1985
5621857	33731143	8	~1985
5621873	33731239	8	~1985
5621899	56218991	8	~1985
5621939	11243879	8	~1984
5622059	44976473	8	~1985
5622251	11244503	8	~1984
5622319	56223191	8	~1985
5622473	33734839	8	~1985
5622479	44979833	8	~1985
5622497	33734983	8	~1985
5622899	11245799	8	~1984
5623099	56230991	8	~1985
5623193	33739159	8	~1985
5623193	179942177	9
5623199	11246399	8	~1984
5623283	11246567	8	~1984
5623283	449862641	9
5623301	33739807	8	~1985
5623619	11247239	8	~1984
5623619	101225143	9
5624039	11248079	8	~1984
5624243	11248487	8	~1984
5624327	101237887	9	~1986
5624471	11248943	8	~1984

5.037.460 digits

25-09-07