Small Mersenne Prime Factors (page 697/5025)

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
5246441	31478647	8	~1985
5246503	125916073	9	~1986
5246519	10493039	8	~1983
5246617	251837617	9	~1987
5246867	94443607	8	~1986
5246873	31481239	8	~1985
5246981	41975849	8	~1985
5247041	31482247	8	~1985
5247083	10494167	8	~1983
5247233	125933593	9	~1986
5247299	10494599	8	~1983
5247391	2518747681	10	~1989
5247461	41979689	8	~1985
5247491	10494983	8	~1983
5247659	10495319	8	~1983
5247919	52479191	8	~1985
5248091	10496183	8	~1983
5248499	10496999	8	~1983
5248499	41987993	8
5248559	41988473	8	~1985
5248583	10497167	8	~1983
5248601	41988809	8	~1985
5249011	52490111	8	~1985
5249051	41992409	8	~1985
5249399	10498799	8	~1983

Exp.	Prime Factor	Digits	Year
5249479	94490623	8	~1986
5249663	10499327	8	~1983
5249683	52496831	8	~1985
5249731	52497311	8	~1985
5249771	136494047	9	~1986
5249813	157494391	9	~1986
5249873	31499239	8	~1985
5249897	31499383	8	~1985
5249903	10499807	8	~1983
5250071	10500143	8	~1983
5250121	378008713	9	~1987
5250391	52503911	8	~1985
5250449	42003593	8	~1985
5250491	10500983	8	~1983
5250743	10501487	8	~1983
5250761	42006089	8	~1985
5250779	10501559	8	~1983
5250803	10501607	8	~1983
5250851	10501703	8	~1983
5251039	220543639	9	~1987
5251097	42008777	8	~1985
5251193	31507159	8	~1985
5251271	10502543	8	~1983
5251663	378119737	9	~1987
5251783	52517831	8	~1985

Exp.	Prime Factor	Digits	Year
5251859	10503719	8	~1983
5251919	42015353	8	~1985
5252281	84036497	8	~1986
5252413	31514479	8	~1985
5252603	10505207	8	~1983
5252761	31516567	8	~1985
5253203	10506407	8	~1983
5253383	10506767	8	~1983
5253431	10506863	8	~1983
5253487	52534871	8	~1985
5253779	10507559	8	~1983
5253881	199647479	9	~1987
5254019	42032153	8	~1985
5254163	10508327	8	~1983
5254247	42033977	8	~1985
5254637	73564919	8	~1986
5254721	31528327	8	~1985
5254831	52548311	8	~1985
5255069	168162209	9	~1986
5255101	31530607	8	~1985
5255113	31530679	8	~1985
5255233	31531399	8	~1985
5255479	52554791	8	~1985
5255527	126132649	9	~1986
5255531	10511063	8	~1983

Exp.	Prime Factor	Digits	Year
5255617	126134809	9	~1986
5255773	84092369	8	~1986
5255819	10511639	8	~1983
5255863	52558631	8	~1985
5256137	31536823	8	~1985
5256239	10512479	8	~1983
5256253	157687591	9	~1986
5256341	31538047	8	~1985
5256371	10512743	8	~1983
5256661	31539967	8	~1985
5256683	10513367	8	~1983
5256751	52567511	8	~1985
5256851	10513703	8	~1983
5257079	10514159	8	~1983
5257157	31542943	8	~1985
5257361	31544167	8	~1985
5257463	10514927	8	~1983
5257793	31546759	8	~1985
5258063	10516127	8	~1983
5258171	10516343	8	~1983
5258171	42065369	8
5258303	10516607	8	~1983
5258399	10516799	8	~1983
5258489	42067913	8	~1985
5258531	10517063	8	~1983

4.724.182 digits

25-04-13