Small Mersenne Prime Factors (page 935/5070)

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
8627903	17255807	8	~1985
8628131	17256263	8	~1985
8628149	120794087	9	~1987
8628677	207088249	9	~1988
8628773	120802823	9	~1987
8628923	17257847	8	~1985
8629139	17258279	8	~1985
8629739	17259479	8	~1985
8629763	17259527	8	~1985
8629813	51778879	8	~1986
8630177	51781063	8	~1986
8630243	17260487	8	~1985
8630519	17261039	8	~1985
8630591	17261183	8	~1985
8630641	51783847	8	~1986
8631017	51786103	8	~1986
8631251	17262503	8	~1985
8631599	17263199	8	~1985
8631851	17263703	8	~1985
8632081	51792487	8	~1986
8632139	17264279	8	~1985
8632223	17264447	8	~1985
8632297	138116753	9	~1987
8632391	17264783	8	~1985
8632451	224443727	9	~1988

Exp.	Prime Factor	Digits	Year
8632457	69059657	8	~1987
8632489	189914759	9	~1988
8632901	69063209	8	~1987
8632979	17265959	8	~1985
8633063	17266127	8	~1985
8633189	120864647	9	~1987
8633231	17266463	8	~1985
8633363	17266727	8	~1985
8633377	51800263	8	~1986
8633711	17267423	8	~1985
8633921	51803527	8	~1986
8634077	51804463	8	~1986
8634371	17268743	8	~1985
8634371	69074969	8
8634397	1018858847	10	~1989
8634803	17269607	8	~1985
8634961	51809767	8	~1986
8635021	51810127	8	~1986
8635043	17270087	8	~1985
8635283	17270567	8	~1985
8635351	86353511	8	~1987
8635579	86355791	8	~1987
8635631	17271263	8	~1985
8635637	69085097	8	~1987
8635951	138175217	9	~1987

Exp.	Prime Factor	Digits	Year
8635999	86359991	8	~1987
8636819	17273639	8	~1985
8636893	259106791	9	~1988
8637107	483677993	9	~1989
8637131	17274263	8	~1985
8637151	138194417	9	~1987
8637263	17274527	8	~1985
8637521	51825127	8	~1986
8637523	86375231	8	~1987
8637749	207305977	9	~1988
8638867	155499607	9	~1987
8639063	17278127	8	~1985
8639381	51836287	8	~1986
8639413	207345913	9	~1988
8639531	17279063	8	~1985
8639837	51839023	8	~1986
8639849	69118793	8	~1987
8639903	17279807	8	~1985
8639921	51839527	8	~1986
8640001	51840007	8	~1986
8640133	51840799	8	~1986
8640161	51840967	8	~1986
8640713	51844279	8	~1986
8640761	51844567	8	~1986
8640967	86409671	8	~1987

Exp.	Prime Factor	Digits	Year
8641063	570310159	9	~1989
8641517	51849103	8	~1986
8641517	69132137	8
8641883	17283767	8	~1985
8641957	3318511489	10	~1991
8642027	155556487	9	~1987
8642189	69137513	8	~1987
8642861	51857167	8	~1986
8643083	17286167	8	~1985
8643143	17286287	8	~1985
8643337	605033591	9	~1989
8643443	17286887	8	~1985
8643521	69148169	8	~1987
8643671	17287343	8	~1985
8643697	51862183	8	~1986
8643839	17287679	8	~1985
8643851	17287703	8	~1985
8643893	121014503	9	~1987
8643941	259318231	9	~1988
8643941	829818337	9
8644019	17288039	8	~1985
8644057	138304913	9	~1987
8644679	17289359	8	~1985
8644949	69159593	8	~1987
8644957	345798281	9	~1988

4.768.925 digits

25-05-04