Small Mersenne Prime Factors (page 941/5610)

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
8213671	131418737	9	~1987
8213819	16427639	8	~1985
8213879	16427759	8	~1985
8214113	114997583	9	~1987
8214209	262854689	9	~1988
8214257	49285543	8	~1986
8214263	16428527	8	~1985
8214343	131429489	9	~1987
8214359	16428719	8	~1985
8214581	49287487	8	~1986
8214779	16429559	8	~1985
8214911	16429823	8	~1985
8215133	49290799	8	~1986
8215247	65721977	8	~1986
8215283	16430567	8	~1985
8215379	16430759	8	~1985
8215969	197183257	9	~1988
8216003	16432007	8	~1985
8216063	16432127	8	~1985
8216231	16432463	8	~1985
8216317	49297903	8	~1986
8216459	16432919	8	~1985
8216471	16432943	8	~1985
8216717	788804833	9	~1989
8216731	82167311	8	~1987

Exp.	Prime Factor	Digits	Year
8217197	49303183	8	~1986
8217227	65737817	8	~1986
8217241	10255116769	11	~1992
8217323	16434647	8	~1985
8217479	16434959	8	~1985
8217551	16435103	8	~1985
8217893	49307359	8	~1986
8218109	65744873	8	~1986
8218753	49312519	8	~1986
8218781	49312687	8	~1986
8218801	49312807	8	~1986
8218993	49313959	8	~1986
8219011	82190111	8	~1987
8219021	263008673	9	~1988
8219591	16439183	8	~1985
8219819	16439639	8	~1985
8220143	16440287	8	~1985
8220203	16440407	8	~1985
8220287	65762297	8	~1986
8220419	65763353	8	~1986
8220791	16441583	8	~1985
8220881	65767049	8	~1986
8221211	16442423	8	~1985
8221331	16442663	8	~1985
8221337	49328023	8	~1986

Exp.	Prime Factor	Digits	Year
8221403	16442807	8	~1985
8221597	49329583	8	~1986
8221859	16443719	8	~1985
8222131	131554097	9	~1987
8222243	16444487	8	~1985
8222413	49334479	8	~1986
8222813	49336879	8	~1986
8222833	49336999	8	~1986
8222959	82229591	8	~1987
8222999	16445999	8	~1985
8223119	16446239	8	~1985
8223251	16446503	8	~1985
8223871	82238711	8	~1987
8223977	49343863	8	~1986
8224031	16448063	8	~1985
8224061	49344367	8	~1986
8224091	16448183	8	~1985
8224529	65796233	8	~1986
8224763	16449527	8	~1985
8224793	49348759	8	~1986
8225039	16450079	8	~1985
8225257	49351543	8	~1986
8225317	49351903	8	~1986
8225351	16450703	8	~1985
8225351	65802809	8

Exp.	Prime Factor	Digits	Year
8225377	394818097	9	~1988
8225431	148057759	9	~1987
8225579	16451159	8	~1985
8225687	65805497	8	~1986
8226143	16452287	8	~1985
8226409	592301449	9	~1989
8226583	82265831	8	~1987
8226593	49359559	8	~1986
8226719	16453439	8	~1985
8226809	65814473	8	~1986
8226857	65814857	8	~1986
8226899	16453799	8	~1985
8226947	65815577	8	~1986
8226947	460709033	9
8227069	394899313	9	~1988
8227217	65817737	8	~1986
8227451	16454903	8	~1985
8227487	148094767	9	~1987
8227559	16455119	8	~1985
8227697	49366183	8	~1986
8227729	197465497	9	~1988
8227811	16455623	8	~1985
8227871	16455743	8	~1985
8228021	65824169	8	~1986
8228201	263302433	9	~1988

5.307.017 digits

26-01-11