Small Mersenne Prime Factors (page 941/5790)

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
8056681	48340087	8	~1986
8056799	16113599	8	~1985
8056859	16113719	8	~1985
8056879	80568791	8	~1987
8057017	48342103	8	~1986
8057561	64460489	8	~1986
8057639	16115279	8	~1985
8057669	112807367	9	~1987
8057893	48347359	8	~1986
8058133	241743991	9	~1988
8058733	48352399	8	~1986
8058899	64471193	8	~1986
8058929	112825007	9	~1987
8059151	16118303	8	~1985
8059193	48355159	8	~1986
8059741	48358447	8	~1986
8060609	64484873	8	~1986
8060681	48364087	8	~1986
8060861	48365167	8	~1986
8060891	16121783	8	~1985
8060939	16121879	8	~1985
8060957	112853399	9	~1987
8061007	80610071	8	~1987
8061289	322451561	9	~1988
8061773	48370639	8	~1986

Exp.	Prime Factor	Digits	Year
8061839	64494713	8	~1986
8062079	16124159	8	~1985
8062451	16124903	8	~1985
8062793	48376759	8	~1986
8062823	16125647	8	~1985
8062979	64503833	8	~1986
8063371	80633711	8	~1987
8063401	48380407	8	~1986
8063597	48381583	8	~1986
8063873	258043937	9	~1988
8063879	16127759	8	~1985
8063963	16127927	8	~1985
8064431	16128863	8	~1985
8064473	48386839	8	~1986
8064517	48387103	8	~1986
8064839	16129679	8	~1985
8065133	48390799	8	~1986
8065391	16130783	8	~1985
8065439	64523513	8	~1986
8065507	322620281	9	~1988
8065679	16131359	8	~1985
8065751	16131503	8	~1985
8066291	16132583	8	~1985
8066291	403314551	9
8066411	145195399	9	~1987

Exp.	Prime Factor	Digits	Year
8066543	16133087	8	~1985
8066761	48400567	8	~1986
8066771	258136673	9	~1988
8066879	16133759	8	~1985
8067023	16134047	8	~1985
8067179	16134359	8	~1985
8067551	16135103	8	~1985
8067679	338842519	9	~1988
8067863	16135727	8	~1985
8067881	48407287	8	~1986
8068019	16136039	8	~1985
8068079	193633897	9	~1988
8068171	145227079	9	~1987
8068223	16136447	8	~1985
8068457	48410743	8	~1986
8068777	193650649	9	~1988
8069531	64556249	8	~1986
8069533	48417199	8	~1986
8070599	16141199	8	~1985
8070857	968502841	9	~1989
8071033	48426199	8	~1986
8071111	129137777	9	~1987
8071127	64569017	8	~1986
8071139	16142279	8	~1985
8071223	16142447	8	~1985

Exp.	Prime Factor	Digits	Year
8071319	64570553	8	~1986
8071463	16142927	8	~1985
8071517	48429103	8	~1986
8072041	48432247	8	~1986
8072111	16144223	8	~1985
8072137	48432823	8	~1986
8072159	145298863	9	~1987
8072171	16144343	8	~1985
8072171	64577369	8
8072591	16145183	8	~1985
8072621	258323873	9	~1988
8073041	64584329	8	~1986
8073077	48438463	8	~1986
8073431	16146863	8	~1985
8073491	16146983	8	~1985
8073817	48442903	8	~1986
8073887	64591097	8	~1986
8073911	16147823	8	~1985
8074013	48444079	8	~1986
8074217	48445303	8	~1986
8074277	64594217	8	~1986
8074637	64597097	8	~1986
8074739	1695695191	10	~1990
8075003	16150007	8	~1985
8075083	129201329	9	~1987

5.486.313 digits

26-04-05