Small Mersenne Prime Factors (page 729/5745)

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
5263733	31582399	8	~1985
5264381	31586287	8	~1985
5264443	84231089	8	~1986
5264477	73702679	8	~1986
5264537	31587223	8	~1985
5264683	52646831	8	~1985
5264801	42118409	8	~1985
5265059	10530119	8	~1984
5265067	52650671	8	~1985
5265131	10530263	8	~1984
5265193	31591159	8	~1985
5265193	115834247	9
5265473	73716623	8	~1986
5266031	10532063	8	~1984
5266271	42130169	8	~1985
5266441	31598647	8	~1985
5266673	31600039	8	~1985
5266799	10533599	8	~1984
5266883	10533767	8	~1984
5266907	42135257	8	~1985
5266979	10533959	8	~1984
5266997	126407929	9	~1986
5267159	221220679	9	~1987
5267257	158017711	9	~1986
5267323	84277169	8	~1986

Exp.	Prime Factor	Digits	Year
5267519	10535039	8	~1984
5267711	10535423	8	~1984
5267783	547849433	9	~1988
5268031	52680311	8	~1985
5268083	10536167	8	~1984
5268119	42144953	8	~1985
5268121	31608727	8	~1985
5268257	42146057	8	~1985
5268293	73756103	8	~1986
5268437	73758119	8	~1986
5268551	10537103	8	~1984
5268671	42149369	8	~1985
5268737	73762319	8	~1986
5268743	10537487	8	~1984
5268779	42150233	8	~1985
5268899	94840183	8	~1986
5268937	31613623	8	~1985
5268953	31613719	8	~1985
5269079	10538159	8	~1984
5269111	84305777	8	~1986
5269259	10538519	8	~1984
5269373	73771223	8	~1986
5269603	632352361	9	~1988
5269787	42158297	8	~1985
5269867	52698671	8	~1985

Exp.	Prime Factor	Digits	Year
5269867	126476809	9
5270029	284581567	9	~1987
5270129	42161033	8	~1985
5270183	10540367	8	~1984
5270537	31623223	8	~1985
5270567	42164537	8	~1985
5270767	52707671	8	~1985
5270773	31624639	8	~1985
5270821	463832249	9	~1988
5271179	42169433	8	~1985
5271319	52713191	8	~1985
5271323	137054399	9	~1986
5271401	42171209	8	~1985
5271463	52714631	8	~1985
5271557	158146711	9	~1986
5271599	10543199	8	~1984
5271719	126521257	9	~1986
5271743	10543487	8	~1984
5272103	10544207	8	~1984
5272237	84355793	8	~1986
5272411	84358577	8	~1986
5272583	10545167	8	~1984
5272637	126543289	9	~1986
5272649	42181193	8	~1985
5272739	390182687	9	~1987

Exp.	Prime Factor	Digits	Year
5272807	84364913	8	~1986
5272979	10545959	8	~1984
5273087	42184697	8	~1985
5273123	10546247	8	~1984
5273531	10547063	8	~1984
5273537	42188297	8	~1985
5273617	84377873	8	~1986
5273711	10547423	8	~1984
5273759	10547519	8	~1984
5273759	126570217	9
5273861	31643167	8	~1985
5274007	52740071	8	~1985
5274023	10548047	8	~1984
5274047	42192377	8	~1985
5274127	84386033	8	~1986
5274257	31645543	8	~1985
5274299	10548599	8	~1984
5274463	52744631	8	~1985
5274623	10549247	8	~1984
5274629	42197033	8	~1985
5274917	31649503	8	~1985
5275021	31650127	8	~1985
5275079	10550159	8	~1984
5275271	10550543	8	~1984
5275561	31653367	8	~1985

5.441.361 digits

26-03-15