Small Mersenne Prime Factors (page 868/5670)

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
7105513	42633079	8	~1986
7105697	42634183	8	~1986
7105993	42635959	8	~1986
7106219	14212439	8	~1985
7106249	56849993	8	~1986
7106299	71062991	8	~1986
7106303	14212607	8	~1985
7106531	56852249	8	~1986
7106639	56853113	8	~1986
7106831	14213663	8	~1985
7106903	14213807	8	~1985
7107137	42642823	8	~1986
7107179	14214359	8	~1985
7107251	14214503	8	~1985
7107371	14214743	8	~1985
7107461	270083519	9	~1988
7107511	7121726023	10	~1991
7107533	42645199	8	~1986
7107677	42646063	8	~1986
7108061	42648367	8	~1986
7108151	14216303	8	~1985
7108259	14216519	8	~1985
7108349	99516887	8	~1987
7108463	14216927	8	~1985
7108583	14217167	8	~1985

Exp.	Prime Factor	Digits	Year
7108583	398080649	9
7108763	14217527	8	~1985
7108823	14217647	8	~1985
7108999	298577959	9	~1988
7109099	14218199	8	~1985
7109099	56872793	8
7109101	42654607	8	~1986
7109107	71091071	8	~1986
7109119	71091191	8	~1986
7109171	14218343	8	~1985
7109197	213275911	9	~1987
7109423	14218847	8	~1985
7109471	56875769	8	~1986
7109561	56876489	8	~1986
7109639	14219279	8	~1985
7109887	71098871	8	~1986
7110119	227523809	9	~1987
7110451	71104511	8	~1986
7110637	42663823	8	~1986
7110659	56885273	8	~1986
7110683	298648687	9	~1988
7110791	14221583	8	~1985
7110877	42665263	8	~1986
7110923	14221847	8	~1985
7111019	170664457	9	~1987

Exp.	Prime Factor	Digits	Year
7111271	14222543	8	~1985
7111463	14222927	8	~1985
7111537	42669223	8	~1986
7111697	99563759	8	~1987
7111877	42671263	8	~1986
7112411	14224823	8	~1985
7112657	42675943	8	~1986
7112663	14225327	8	~1985
7112711	14225423	8	~1985
7112717	42676303	8	~1986
7112731	71127311	8	~1986
7112761	42676567	8	~1986
7112939	14225879	8	~1985
7113053	42678319	8	~1986
7113061	113808977	9	~1987
7113101	42678607	8	~1986
7113311	14226623	8	~1985
7113563	14227127	8	~1985
7113611	14227223	8	~1985
7113661	42681967	8	~1986
7113719	14227439	8	~1985
7113721	42682327	8	~1986
7113763	71137631	8	~1986
7113793	213413791	9	~1987
7113913	42683479	8	~1986

Exp.	Prime Factor	Digits	Year
7113913	512201737	9
7113941	42683647	8	~1986
7114231	71142311	8	~1986
7114277	56914217	8	~1986
7114649	56917193	8	~1986
7115051	14230103	8	~1985
7115057	42690343	8	~1986
7115117	56920937	8	~1986
7115153	42690919	8	~1986
7115219	14230439	8	~1985
7115347	71153471	8	~1986
7115351	14230703	8	~1985
7115357	56922857	8	~1986
7115477	56923817	8	~1986
7115539	71155391	8	~1986
7115593	42693559	8	~1986
7115819	56926553	8	~1986
7116023	14232047	8	~1985
7116299	14232599	8	~1985
7116311	14232623	8	~1985
7116899	14233799	8	~1985
7117501	42705007	8	~1986
7117637	56941097	8	~1986
7117717	42706303	8	~1986
7117823	227770337	9	~1987

5.366.787 digits

26-02-08