Small Mersenne Prime Factors (page 564/5730)

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
3464807	256395719	9	~1986
3465101	20790607	8	~1983
3465151	55442417	8	~1984
3465257	20791543	8	~1983
3465373	55445969	8	~1984
3465379	34653791	8	~1984
3465491	62378839	8	~1984
3465503	6931007	7	~1982
3465731	90109007	8	~1985
3465857	20795143	8	~1983
3465857	83180569	8
3465947	27727577	8	~1984
3465989	48523847	8	~1984
3466321	20797927	8	~1983
3466343	83192233	8	~1985
3466499	6932999	7	~1982
3466601	20799607	8	~1983
3466613	110931617	9	~1985
3466643	6933287	7	~1982
3466763	6933527	7	~1982
3466811	6933623	7	~1982
3466811	27734489	8
3466933	55470929	8	~1984
3466943	6933887	7	~1982
3467297	332860513	9	~1986

Exp.	Prime Factor	Digits	Year
3467543	6935087	7	~1982
3467593	20805559	8	~1983
3467647	83223529	8	~1985
3467669	27741353	8	~1984
3467693	48547703	8	~1984
3467909	27743273	8	~1984
3468301	305210489	9	~1986
3468307	34683071	8	~1984
3468359	6936719	7	~1982
3468481	20810887	8	~1983
3468599	27748793	8	~1984
3468863	6937727	7	~1982
3468991	62441839	8	~1984
3469019	6938039	7	~1982
3469061	27752489	8	~1984
3469073	20814439	8	~1983
3469181	20815087	8	~1983
3469223	6938447	7	~1982
3469247	27753977	8	~1984
3469387	55510193	8	~1984
3469393	20816359	8	~1983
3469421	20816527	8	~1983
3469421	27755369	8
3469519	62451343	8	~1984
3469867	62457607	8	~1984

Exp.	Prime Factor	Digits	Year
3469943	6939887	7	~1982
3470003	6940007	7	~1982
3470161	20820967	8	~1983
3470239	117988127	9	~1985
3470353	55525649	8	~1984
3470443	55527089	8	~1984
3470587	34705871	8	~1984
3470617	20823703	8	~1983
3470821	20824927	8	~1983
3470851	34708511	8	~1984
3470891	62476039	8	~1984
3471059	6942119	7	~1982
3471317	48598439	8	~1984
3471569	27772553	8	~1984
3471607	62488927	8	~1984
3471617	20829703	8	~1983
3471719	6943439	7	~1982
3471883	145819087	9	~1985
3471959	6943919	7	~1982
3472223	645833479	9	~1987
3472247	62500447	8	~1984
3472319	62501743	8	~1984
3472349	83336377	8	~1985
3472499	6944999	7	~1982
3472523	6945047	7	~1982

Exp.	Prime Factor	Digits	Year
3472583	6945167	7	~1982
3472739	6945479	7	~1982
3472883	90294959	8	~1985
3472951	62513119	8	~1984
3472979	6945959	7	~1982
3473033	20838199	8	~1983
3473221	20839327	8	~1983
3473297	27786377	8	~1984
3473297	187558039	9
3473753	20842519	8	~1983
3474071	6948143	7	~1982
3474167	62535007	8	~1984
3474257	20845543	8	~1983
3474257	132021767	9
3474323	6948647	7	~1982
3474599	6949199	7	~1982
3474599	27796793	8
3474623	6949247	7	~1982
3474631	62543359	8	~1984
3474719	27797753	8	~1984
3474797	27798377	8	~1984
3474893	632430527	9	~1987
3474899	6949799	7	~1982
3475057	20850343	8	~1983
3475079	6950159	7	~1982

5.426.516 digits

26-03-08