Small Mersenne Prime Factors (page 890/5205)

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
7785803	15571607	8	~1985
7785913	46715479	8	~1986
7786151	15572303	8	~1985
7786451	15572903	8	~1985
7786511	15573023	8	~1985
7786763	15573527	8	~1985
7786873	46721239	8	~1986
7787183	15574367	8	~1985
7787291	15574583	8	~1985
7787303	15574607	8	~1985
7787441	62299529	8	~1986
7787537	46725223	8	~1986
7787677	46726063	8	~1986
7787699	62301593	8	~1986
7787771	15575543	8	~1985
7787951	62303609	8	~1986
7788181	46729087	8	~1986
7788259	77882591	8	~1987
7788631	77886311	8	~1987
7788857	623108561	9	~1989
7789073	46734439	8	~1986
7789079	15578159	8	~1985
7789189	13646659129	11	~1992
7789253	46735519	8	~1986
7789343	15578687	8	~1985

Exp.	Prime Factor	Digits	Year
7789363	124629809	9	~1987
7789403	15578807	8	~1985
7789469	482947079	9	~1988
7789583	15579167	8	~1985
7789841	2352531983	10	~1990
7789919	62319353	8	~1986
7789997	46739983	8	~1986
7790423	15580847	8	~1985
7790459	15580919	8	~1985
7790591	15581183	8	~1985
7790639	62325113	8	~1986
7790897	46745383	8	~1986
7790903	15581807	8	~1985
7791239	62329913	8	~1986
7791379	77913791	8	~1987
7791493	46748959	8	~1986
7791551	15583103	8	~1985
7791677	46750063	8	~1986
7791697	46750183	8	~1986
7791911	15583823	8	~1985
7791911	62335289	8
7793153	46758919	8	~1986
7793231	62345849	8	~1986
7793459	15586919	8	~1985
7793473	46760839	8	~1986

Exp.	Prime Factor	Digits	Year
7793759	15587519	8	~1985
7794071	15588143	8	~1985
7794323	15588647	8	~1985
7794643	498857153	9	~1988
7794863	15589727	8	~1985
7794929	62359433	8	~1986
7794971	62359769	8	~1986
7795223	15590447	8	~1985
7795237	46771423	8	~1986
7795439	15590879	8	~1985
7795559	62364473	8	~1986
7795661	46773967	8	~1986
7795687	77956871	8	~1987
7795811	15591623	8	~1985
7796003	15592007	8	~1985
7796071	77960711	8	~1987
7796111	140329999	9	~1987
7796611	77966111	8	~1987
7796699	15593399	8	~1985
7797071	15594143	8	~1985
7797241	46783447	8	~1986
7797311	62378489	8	~1986
7797401	46784407	8	~1986
7797487	265114559	9	~1988
7797593	46785559	8	~1986

Exp.	Prime Factor	Digits	Year
7797701	62381609	8	~1986
7797743	15595487	8	~1985
7797877	46787263	8	~1986
7797983	15595967	8	~1985
7798397	46790383	8	~1986
7798463	15596927	8	~1985
7798621	46791727	8	~1986
7798717	46792303	8	~1986
7798793	748684129	9	~1989
7798811	15597623	8	~1985
7798859	62390873	8	~1986
7798963	77989631	8	~1987
7799111	15598223	8	~1985
7799201	46795207	8	~1986
7799201	62393609	8
7799339	15598679	8	~1985
7799459	62395673	8	~1986
7799513	249584417	9	~1988
7799723	15599447	8	~1985
7799797	46798783	8	~1986
7799843	15599687	8	~1985
7800119	15600239	8	~1985
7800137	46800823	8	~1986
7800791	62406329	8	~1986
7800959	15601919	8	~1985

4.903.097 digits

25-07-08