Small Mersenne Prime Factors (page 1/4260)

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
1	1	1	~-430
3	7	1	~-430
5	31	2	~-300
7	127	3	~-300
11	23	2	1536
11	89	2
13	8191	4	1456
17	131071	6	1588
19	524287	6	1588
23	47	2	1640
23	178481	6
29	233	3	1733
29	1103	4
29	2089	4
31	2147483647	10	1772
37	223	3	1640
37	616318177	9
41	13367	5	1859
41	164511353	9
43	431	3	1733
43	9719	4
43	2099863	7
47	2351	4	1741
47	4513	4
47	13264529	8

Exp.	Prime Factor	Digits	Year
53	6361	4	1867
53	69431	5
53	20394401	8
59	179951	6	1869
61	2305...693951	19	1883
71	228479	6	1909
71	48544121	8
73	439	3	1733
73	2298041	7
79	2687	4	1856
83	167	3	1732
89	6189...562111	27	1911
97	11447	5	1881
107	1622...288127	33	1914
113	3391	4	1856
113	23279	5
113	65993	5
113	1868569	7
127	1701...105727	39	1876
131	263	3	1733
151	18121	5	1881
151	55871	5
151	165799	6
151	2332951	7
163	150287	6	1908

Exp.	Prime Factor	Digits	Year
163	704161	6
167	2349023	7	1946
173	730753	6	1912
173	1505447	7
179	359	3	1733
179	1433	4
181	43441	5	1911
181	1164193	7
181	7648337	7
191	383	3	1733
193	13821503	8	1960
197	7487	4	1895
211	15193	5	1881
223	18287	5	1881
223	196687	6
223	1466449	7
223	2916841	7
229	1504073	7	1946
229	20492753	8
233	1399	4	1856
233	135607	6
233	622577	6
239	479	3	1733
239	1913	4
239	5737	4

Exp.	Prime Factor	Digits	Year
239	176383	6
241	22000409	8	1960
251	503	3	1733
251	54217	5
263	23671	5	1952
269	13822297	8	1960
277	1121297	7	1957
281	80929	5	1952
283	9623	4	1952
307	14608903	8	1960
307	85798519	8
311	5344847	7	1957
313	10960009	8	1960
317	9511	4	1952
337	18199	5	1952
337	2806537	7
353	931921	6	1952
359	719	3	1952
359	855857	6
367	12479	5	1952
367	51791041	8
373	25569151	8	1960
373	7524...458241	105	2005
379	6809...894953	103	2005
383	1440847	7	1957

3.968.152 digits

24-04-21