Small Mersenne Prime Factors (page 897/5025)

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
8049113	450750329	9	~1988
8049221	48295327	8	~1986
8049383	16098767	8	~1985
8049803	16099607	8	~1985
8050103	450805769	9	~1988
8050291	80502911	8	~1987
8050439	16100879	8	~1985
8050711	80507111	8	~1987
8050961	48305767	8	~1986
8051171	16102343	8	~1985
8051651	16103303	8	~1985
8051677	48310063	8	~1986
8051713	48310279	8	~1986
8051713	241551391	9
8051959	80519591	8	~1987
8052431	16104863	8	~1985
8052433	48314599	8	~1986
8052683	16105367	8	~1985
8052817	48316903	8	~1986
8053007	64424057	8	~1986
8053043	16106087	8	~1985
8053091	16106183	8	~1985
8053351	128853617	9	~1987
8053757	48322543	8	~1986
8053757	64430057	8

Exp.	Prime Factor	Digits	Year
8053763	16107527	8	~1985
8053807	80538071	8	~1987
8054471	16108943	8	~1985
8054471	64435769	8
8054609	64436873	8	~1986
8054741	48328447	8	~1986
8054881	48329287	8	~1986
8054881	128878097	9
8054939	16109879	8	~1985
8055143	16110287	8	~1985
8055193	48331159	8	~1986
8055473	451106489	9	~1988
8055959	16111919	8	~1985
8056033	48336199	8	~1986
8056211	16112423	8	~1985
8056259	16112519	8	~1985
8056261	48337567	8	~1986
8056271	16112543	8	~1985
8056679	16113359	8	~1985
8056681	48340087	8	~1986
8056799	16113599	8	~1985
8056859	16113719	8	~1985
8057017	48342103	8	~1986
8057561	64460489	8	~1986
8057639	16115279	8	~1985

Exp.	Prime Factor	Digits	Year
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
8061839	64494713	8	~1986
8062079	16124159	8	~1985
8062451	16124903	8	~1985
8062793	48376759	8	~1986
8062823	16125647	8	~1985
8063371	80633711	8	~1987
8063401	48380407	8	~1986

Exp.	Prime Factor	Digits	Year
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
8065679	16131359	8	~1985
8065751	16131503	8	~1985
8066291	16132583	8	~1985
8066291	403314551	9
8066411	145195399	9	~1987
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
8067863	16135727	8	~1985
8067881	48407287	8	~1986
8068019	16136039	8	~1985

4.724.182 digits

25-04-13