Small Mersenne Prime Factors (page 943/5025)

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
8817839	17635679	8	~1985
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
8821919	17643839	8	~1985
8821979	17643959	8	~1985
8822161	52932967	8	~1986
8822171	17644343	8	~1985
8822189	70577513	8	~1987

Exp.	Prime Factor	Digits	Year
8822291	282313313	9	~1988
8822533	52935199	8	~1986
8822623	88226231	8	~1987
8822843	17645687	8	~1985
8822939	17645879	8	~1985
8823293	52939759	8	~1986
8823413	264702391	9	~1988
8823539	17647079	8	~1985
8823553	52941319	8	~1986
8823653	52941919	8	~1986
8823707	70589657	8	~1987
8823719	652955207	9	~1989
8823791	17647583	8	~1985
8823851	17647703	8	~1985
8824229	211781497	9	~1988
8824583	17649167	8	~1985
8824811	17649623	8	~1985
8825213	52951279	8	~1986
8825231	17650463	8	~1985
8825263	88252631	8	~1987
8825321	70602569	8	~1987
8825543	17651087	8	~1985
8825561	70604489	8	~1987
8825651	17651303	8	~1985
8825819	17651639	8	~1985

Exp.	Prime Factor	Digits	Year
8825891	17651783	8	~1985
8826019	88260191	8	~1987
8826221	52957327	8	~1986
8826253	52957519	8	~1986
8826371	17652743	8	~1985
8826593	52959559	8	~1986
8826793	52960759	8	~1986
8826899	17653799	8	~1985
8826977	52961863	8	~1986
8827103	17654207	8	~1985
8827391	17654783	8	~1985
8827691	17655383	8	~1985
8828063	17656127	8	~1985
8828191	141251057	9	~1987
8828279	17656559	8	~1985
8828381	70627049	8	~1987
8828471	17656943	8	~1985
8828639	17657279	8	~1985
8829143	282532577	9	~1988
8829257	52975543	8	~1986
8829371	17658743	8	~1985
8829503	17659007	8	~1985
8829839	17659679	8	~1985
8829869	335535023	9	~1988
8830103	17660207	8	~1985

Exp.	Prime Factor	Digits	Year
8830271	17660543	8	~1985
8830279	88302791	8	~1987
8830357	52982143	8	~1986
8830559	70644473	8	~1987
8830559	370883479	9
8830823	17661647	8	~1985
8831047	88310471	8	~1987
8831111	17662223	8	~1985
8831191	88311911	8	~1987
8831309	70650473	8	~1987
8831351	17662703	8	~1985
8831353	52988119	8	~1986
8831569	1677998111	10	~1990
8831783	17663567	8	~1985
8832149	70657193	8	~1987
8832203	17664407	8	~1985
8832431	17664863	8	~1985
8832497	52994983	8	~1986
8832521	52995127	8	~1986
8832581	70660649	8	~1987
8832623	17665247	8	~1985
8832779	17665559	8	~1985
8833091	17666183	8	~1985
8833117	52998703	8	~1986
8833277	52999663	8	~1986

4.724.182 digits

25-04-13