Small Mersenne Prime Factors (page 907/5205)

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
8036711	16073423	8	~1985
8036939	16073879	8	~1985
8037187	144669367	9	~1987
8037269	64298153	8	~1986
8037569	112525967	9	~1987
8037851	64302809	8	~1986
8038343	29388182009	11	~1993
8038451	16076903	8	~1985
8038571	16077143	8	~1985
8038631	16077263	8	~1985
8038697	64309577	8	~1986
8039501	64316009	8	~1986
8039789	64318313	8	~1986
8039879	64319033	8	~1986
8039939	16079879	8	~1985
8040029	64320233	8	~1986
8040089	192962137	9	~1988
8040491	16080983	8	~1985
8040671	144732079	9	~1987
8040757	48244543	8	~1986
8040839	16081679	8	~1985
8041333	771967969	9	~1989
8041499	16082999	8	~1985
8041571	16083143	8	~1985
8041577	48249463	8	~1986

Exp.	Prime Factor	Digits	Year
8041717	48250303	8	~1986
8042093	48252559	8	~1986
8042701	48256207	8	~1986
8042711	16085423	8	~1985
8042897	48257383	8	~1986
8043187	128690993	9	~1987
8043401	64347209	8	~1986
8043611	16087223	8	~1985
8043683	16087367	8	~1985
8043877	48263263	8	~1986
8043923	16087847	8	~1985
8043929	64351433	8	~1986
8044061	48264367	8	~1986
8044061	64352489	8
8044079	16088159	8	~1985
8044103	16088207	8	~1985
8044259	16088519	8	~1985
8044331	16088663	8	~1985
8044559	16089119	8	~1985
8044703	16089407	8	~1985
8044877	64359017	8	~1986
8044931	16089863	8	~1985
8045153	48270919	8	~1986
8045183	16090367	8	~1985
8045381	305724479	9	~1988

Exp.	Prime Factor	Digits	Year
8045509	193092217	9	~1988
8045657	48273943	8	~1986
8045701	128731217	9	~1987
8045857	128733713	9	~1987
8045951	64367609	8	~1986
8046013	48276079	8	~1986
8046023	8898901439	10	~1992
8046161	64369289	8	~1986
8046299	16092599	8	~1985
8046497	48278983	8	~1986
8047261	48283567	8	~1986
8047331	64378649	8	~1986
8047399	515033537	9	~1989
8048363	16096727	8	~1985
8048657	64389257	8	~1986
8048849	64390793	8	~1986
8048969	64391753	8	~1986
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

Exp.	Prime Factor	Digits	Year
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
8053349	64426793	8	~1986
8053351	128853617	9	~1987
8053757	48322543	8	~1986
8053757	64430057	8
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

4.903.097 digits

25-07-08