Small Mersenne Prime Factors (page 422/6045)

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
2176679	17413433	8	~1982
2176807	74011439	8	~1984
2176817	30475439	8	~1983
2176871	4353743	7	~1981
2176873	13061239	8	~1982
2176921	47892263	8	~1983
2177083	34833329	8	~1983
2177101	13062607	8	~1982
2177297	13063783	8	~1982
2177353	52256473	8	~1983
2177449	87097961	8	~1984
2177453	13064719	8	~1982
2177573	30486023	8	~1983
2177957	82762367	8	~1984
2177999	4355999	7	~1981
2178083	4356167	7	~1981
2178131	91481503	8	~1984
2178133	13068799	8	~1982
2178149	69700769	8	~1983
2178151	21781511	8	~1982
2178151	39206719	8
2178383	4356767	7	~1981
2178439	21784391	8	~1982
2178443	4356887	7	~1981
2178557	13071343	8	~1982

Exp.	Prime Factor	Digits	Year
2178679	39216223	8	~1983
2178947	39221047	8	~1983
2179139	4358279	7	~1981
2179139	69732449	8
2179223	4358447	7	~1981
2179763	4359527	7	~1981
2179769	17438153	8	~1982
2179823	4359647	7	~1981
2179997	30519959	8	~1983
2180039	4360079	7	~1981
2180071	34881137	8	~1983
2180111	17440889	8	~1982
2180111	69763553	8
2180119	104645713	9	~1984
2180219	4360439	7	~1981
2180293	87211721	8	~1984
2180293	117735823	9
2180351	4360703	7	~1981
2180389	87215561	8	~1984
2180491	348878561	9	~1985
2180543	4361087	7	~1981
2180603	4361207	7	~1981
2180603	157003417	9
2180723	52337353	8	~1983
2180873	13085239	8	~1982

Exp.	Prime Factor	Digits	Year
2180911	21809111	8	~1982
2181017	104688817	9	~1984
2181071	17448569	8	~1982
2181097	366424297	9	~1985
2181149	30536087	8	~1983
2181173	65435191	8	~1983
2181359	4362719	7	~1981
2181379	52353097	8	~1983
2181461	13088767	8	~1982
2181539	17452313	8	~1982
2181541	87261641	8	~1984
2181601	34905617	8	~1983
2181611	4363223	7	~1981
2181659	4363319	7	~1981
2181671	39270079	8	~1983
2181719	4363439	7	~1981
2181919	52366057	8	~1983
2182009	65460271	8	~1983
2182199	91652359	8	~1984
2182259	4364519	7	~1981
2182259	17458073	8
2182451	17459609	8	~1982
2182529	30555407	8	~1983
2182573	48016607	8	~1983
2182811	4365623	7	~1981

Exp.	Prime Factor	Digits	Year
2182937	17463497	8	~1982
2183117	52394809	8	~1983
2183287	21832871	8	~1982
2183453	13100719	8	~1982
2183521	34936337	8	~1983
2183543	4367087	7	~1981
2183579	4367159	7	~1981
2183749	117922447	9	~1984
2183809	52411417	8	~1983
2183899	91723759	8	~1984
2183957	65518711	8	~1983
2183959	21839591	8	~1982
2183963	4367927	7	~1981
2184001	34944017	8	~1983
2184179	4368359	7	~1981
2184263	4368527	7	~1981
2184293	30580103	8	~1983
2184323	69898337	8	~1983
2184397	13106383	8	~1982
2184641	13107847	8	~1982
2184641	17477129	8
2184647	17477177	8	~1982
2184877	13109263	8	~1982
2184967	21849671	8	~1982
2184967	1245431191	10

5.740.663 digits

26-08-02