Small Mersenne Prime Factors (page 868/5460)

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
7247257	43483543	8	~1986
7247291	14494583	8	~1985
7247333	739227967	9	~1989
7247351	14494703	8	~1985
7247393	43484359	8	~1986
7247927	130462687	9	~1987
7248119	14496239	8	~1985
7248251	57986009	8	~1986
7248299	57986393	8	~1986
7248379	72483791	8	~1986
7248497	43490983	8	~1986
7248653	217459591	9	~1987
7248739	72487391	8	~1986
7248821	43492927	8	~1986
7248881	43493287	8	~1986
7249093	115985489	9	~1987
7249211	14498423	8	~1985
7249337	43496023	8	~1986
7249441	43496647	8	~1986
7249523	14499047	8	~1985
7249573	115993169	9	~1987
7249841	43499047	8	~1986
7249919	14499839	8	~1985
7249943	14499887	8	~1985
7250051	14500103	8	~1985

Exp.	Prime Factor	Digits	Year
7250189	58001513	8	~1986
7250231	14500463	8	~1985
7250291	14500583	8	~1985
7250339	14500679	8	~1985
7250363	14500727	8	~1985
7250717	58005737	8	~1986
7250861	58006889	8	~1986
7251011	58008089	8	~1986
7251059	14502119	8	~1985
7251091	130519639	9	~1987
7251311	14502623	8	~1985
7251317	43507903	8	~1986
7251599	14503199	8	~1985
7251691	290067641	9	~1988
7251757	43510543	8	~1986
7251791	14503583	8	~1985
7252187	58017497	8	~1986
7252381	43514287	8	~1986
7252501	43515007	8	~1986
7252571	14505143	8	~1985
7252631	14505263	8	~1985
7253063	174073513	9	~1987
7253531	14507063	8	~1985
7253669	232117409	9	~1988
7253837	43523023	8	~1986

Exp.	Prime Factor	Digits	Year
7253941	43523647	8	~1986
7253957	58031657	8	~1986
7254179	14508359	8	~1985
7254419	14508839	8	~1985
7254617	43527703	8	~1986
7254743	14509487	8	~1985
7254761	43528567	8	~1986
7254803	188624879	9	~1987
7255019	14510039	8	~1985
7255067	58040537	8	~1986
7255151	14510303	8	~1985
7255693	43534159	8	~1986
7255763	14511527	8	~1985
7255951	130607119	9	~1987
7255979	58047833	8	~1986
7256393	43538359	8	~1986
7256519	58052153	8	~1986
7256591	14513183	8	~1985
7256593	682119743	9	~1989
7256849	58054793	8	~1986
7256999	14513999	8	~1985
7257023	14514047	8	~1985
7257137	43542823	8	~1986
7257179	14514359	8	~1985
7257253	159659567	9	~1987

Exp.	Prime Factor	Digits	Year
7257311	14514623	8	~1985
7257707	58061657	8	~1986
7257781	43546687	8	~1986
7257851	14515703	8	~1985
7258093	43548559	8	~1986
7258319	14516639	8	~1985
7258661	58069289	8	~1986
7258943	14517887	8	~1985
7259041	987229577	9	~1989
7259519	14519039	8	~1985
7259783	14519567	8	~1985
7259801	43558807	8	~1986
7259869	159717119	9	~1987
7259977	43559863	8	~1986
7260083	14520167	8	~1985
7260119	14520239	8	~1985
7260191	188764967	9	~1987
7261283	14522567	8	~1985
7261349	58090793	8	~1986
7261381	290455241	9	~1988
7261451	14522903	8	~1985
7261511	14523023	8	~1985
7261679	14523359	8	~1985
7261949	58095593	8	~1986
7261949	101667287	9

5.157.210 digits

25-11-02