Small Mersenne Prime Factors (page 745/5460)

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
5608199	11216399	8	~1984
5608217	33649303	8	~1985
5608327	56083271	8	~1985
5608703	11217407	8	~1984
5608903	89742449	8	~1986
5609141	33654847	8	~1985
5609183	11218367	8	~1984
5609231	11218463	8	~1984
5609657	44877257	8	~1985
5609713	33658279	8	~1985
5609783	11219567	8	~1984
5609951	11219903	8	~1984
5610161	44881289	8	~1985
5610197	33661183	8	~1985
5610233	78543263	8	~1986
5610461	33662767	8	~1985
5610469	168314071	9	~1987
5610653	33663919	8	~1985
5610797	44886377	8	~1985
5610887	44887097	8	~1985
5610977	78553679	8	~1986
5611019	11222039	8	~1984
5611043	11222087	8	~1984
5611223	11222447	8	~1984
5611721	33670327	8	~1985

Exp.	Prime Factor	Digits	Year
5611841	33671047	8	~1985
5611871	11223743	8	~1984
5612107	56121071	8	~1985
5612111	11224223	8	~1984
5612221	33673327	8	~1985
5612249	78571487	8	~1986
5612291	11224583	8	~1984
5612339	11224679	8	~1984
5612423	11224847	8	~1984
5612447	44899577	8	~1985
5612591	11225183	8	~1984
5612609	44900873	8	~1985
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

Exp.	Prime Factor	Digits	Year
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
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

Exp.	Prime Factor	Digits	Year
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
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

5.157.210 digits

25-11-02