Small Mersenne Prime Factors (page 955/5205)

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
8804267	70434137	8	~1987
8804303	17608607	8	~1985
8804437	52826623	8	~1986
8804591	17609183	8	~1985
8804843	17609687	8	~1985
8804891	17609783	8	~1985
8804897	52829383	8	~1986
8804953	52829719	8	~1986
8805011	17610023	8	~1985
8805143	17610287	8	~1985
8805323	17610647	8	~1985
8805523	140888369	9	~1987
8805773	123280823	9	~1987
8805913	140894609	9	~1987
8806043	17612087	8	~1985
8806073	52836439	8	~1986
8806093	52836559	8	~1986
8806403	17612807	8	~1985
8806439	17612879	8	~1985
8806757	70454057	8	~1987
8806859	17613719	8	~1985
8807273	52843639	8	~1986
8807681	70461449	8	~1987
8807993	52847959	8	~1986
8808623	17617247	8	~1985

Exp.	Prime Factor	Digits	Year
8808967	158561407	9	~1988
8809057	140944913	9	~1987
8809063	140945009	9	~1987
8809259	158566663	9	~1988
8809967	70479737	8	~1987
8809991	17619983	8	~1985
8809993	52859959	8	~1986
8810099	17620199	8	~1985
8810183	17620367	8	~1985
8810279	70482233	8	~1987
8810309	70482473	8	~1987
8810401	140966417	9	~1987
8810441	52862647	8	~1986
8810663	17621327	8	~1985
8810873	123352223	9	~1987
8810891	70487129	8	~1987
8810993	52865959	8	~1986
8811007	140976113	9	~1987
8811251	17622503	8	~1985
8811359	17622719	8	~1985
8811373	52868239	8	~1986
8811479	17622959	8	~1985
8811851	17623703	8	~1985
8812439	17624879	8	~1985
8812673	52876039	8	~1986

Exp.	Prime Factor	Digits	Year
8812961	70503689	8	~1987
8813107	793179631	9	~1989
8813543	17627087	8	~1985
8813639	17627279	8	~1985
8813771	17627543	8	~1985
8813993	52883959	8	~1986
8814479	17628959	8	~1985
8814479	70515833	8
8814671	17629343	8	~1985
8814851	370223743	9	~1988
8814913	52889479	8	~1986
8815021	52890127	8	~1986
8815063	88150631	8	~1987
8815283	17630567	8	~1985
8815403	17630807	8	~1985
8815421	52892527	8	~1986
8815769	70526153	8	~1987
8815973	52895839	8	~1986
8816243	17632487	8	~1985
8816303	17632607	8	~1985
8816317	52897903	8	~1986
8816317	211591609	9
8816579	440828951	9	~1989
8816987	70535897	8	~1987
8817023	17634047	8	~1985

Exp.	Prime Factor	Digits	Year
8817077	70536617	8	~1987
8817241	52903447	8	~1986
8817541	52905247	8	~1986
8817563	17635127	8	~1985
8817839	17635679	8	~1985
8817839	70542713	8
8817863	17635727	8	~1985
8818037	70544297	8	~1987
8818253	211638073	9	~1988
8818673	52912039	8	~1986
8818681	52912087	8	~1986
8818811	17637623	8	~1985
8819003	17638007	8	~1985
8819191	88191911	8	~1987
8819351	17638703	8	~1985
8819423	17638847	8	~1985
8819467	88194671	8	~1987
8819561	52917367	8	~1986
8819621	52917727	8	~1986
8820041	52920247	8	~1986
8820083	17640167	8	~1985
8820299	17640599	8	~1985
8820803	17641607	8	~1985
8820961	52925767	8	~1986
8821313	123498383	9	~1987

4.903.097 digits

25-07-08