Small Mersenne Prime Factors (page 349/5010)

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
1739347	100882127	9	~1983
1739359	31308463	8	~1982
1739443	17394431	8	~1981
1739533	10437199	8	~1981
1739603	3479207	7	~1980
1739609	316608839	9	~1985
1739653	41751673	8	~1982
1739869	38277119	8	~1982
1739891	3479783	7	~1980
1739911	17399111	8	~1981
1739957	13919657	8	~1981
1740041	177484183	9	~1984
1740241	10441447	8	~1981
1740257	13922057	8	~1981
1740259	17402591	8	~1981
1740293	24364103	8	~1982
1740367	17403671	8	~1981
1740379	41769097	8	~1982
1740379	59172887	8
1740503	3481007	7	~1980
1740691	184513247	9	~1984
1740701	52221031	8	~1983
1740731	3481463	7	~1980
1740779	3481559	7	~1980
1740811	69632441	8	~1983

Exp.	Prime Factor	Digits	Year
1740881	10445287	8	~1981
1740911	3481823	7	~1980
1741013	41784313	8	~1982
1741079	3482159	7	~1980
1741079	13928633	8
1741099	31339783	8	~1982
1741241	10447447	8	~1981
1741339	17413391	8	~1981
1741387	17413871	8	~1981
1741517	13932137	8	~1981
1741687	17416871	8	~1981
1741979	3483959	7	~1980
1742249	52267471	8	~1983
1742369	24393167	8	~1982
1742393	10454359	8	~1981
1742401	10454407	8	~1981
1742501	10455007	8	~1981
1742579	3485159	7	~1980
1742791	31370239	8	~1982
1742843	3485687	7	~1980
1742941	10457647	8	~1981
1743013	41832313	8	~1982
1743047	13944377	8	~1981
1743113	24403583	8	~1982
1743149	13945193	8	~1981

Exp.	Prime Factor	Digits	Year
1743179	139454321	9	~1984
1743221	13945769	8	~1981
1743317	4794121751	10	~1987
1743419	3486839	7	~1980
1743473	55791137	8	~1983
1743737	10462423	8	~1981
1743803	3487607	7	~1980
1743803	41851273	8
1743829	38364239	8	~1982
1743869	13950953	8	~1981
1743919	101147303	9	~1983
1744097	10464583	8	~1981
1744111	27905777	8	~1982
1744357	10466143	8	~1981
1744363	17443631	8	~1981
1744493	24422903	8	~1982
1744517	3024992479	10	~1987
1744621	27913937	8	~1982
1744643	3489287	7	~1980
1744777	10468663	8	~1981
1744817	13958537	8	~1981
1745087	13960697	8	~1981
1745111	55843553	8	~1983
1745197	10471183	8	~1981
1745231	3490463	7	~1980

Exp.	Prime Factor	Digits	Year
1745257	10471543	8	~1981
1745351	3490703	7	~1980
1745389	38398559	8	~1982
1745461	10472767	8	~1981
1745489	13963913	8	~1981
1745501	13964009	8	~1981
1745699	55862369	8	~1983
1745753	55864097	8	~1983
1745969	55871009	8	~1983
1746109	52383271	8	~1983
1746203	3492407	7	~1980
1746209	13969673	8	~1981
1746209	24446927	8
1746209	41909017	8
1746259	41910217	8	~1982
1746301	10477807	8	~1981
1746539	41916937	8	~1982
1746557	24451799	8	~1982
1746587	181645049	9	~1984
1746683	3493367	7	~1980
1746847	17468471	8	~1981
1746883	41925193	8	~1982
1746907	27950513	8	~1982
1746911	13975289	8	~1981
1747079	3494159	7	~1980

4.709.457 digits

25-04-06