Small Mersenne Prime Factors (page 418/5025)

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
2292881	18343049	8	~1982
2292949	91717961	8	~1984
2293103	4586207	7	~1981
2293121	18344969	8	~1982
2293127	18345017	8	~1982
2293219	22932191	8	~1982
2293267	22932671	8	~1982
2293393	13760359	8	~1982
2293559	4587119	7	~1981
2293751	4587503	7	~1981
2293799	4587599	7	~1981
2293847	18350777	8	~1982
2293877	13763263	8	~1982
2293901	18351209	8	~1982
2293919	18351353	8	~1982
2293957	36703313	8	~1983
2294177	68825311	8	~1984
2294477	32122679	8	~1983
2294659	55071817	8	~1983
2294671	41304079	8	~1983
2294693	13768159	8	~1982
2294731	22947311	8	~1982
2294819	4589639	7	~1981
2294879	4589759	7	~1981
2295079	22950791	8	~1982

Exp.	Prime Factor	Digits	Year
2295233	13771399	8	~1982
2295253	13771519	8	~1982
2295361	13772167	8	~1982
2295479	4590959	7	~1981
2295479	55091497	8
2295539	4591079	7	~1981
2295659	4591319	7	~1981
2295673	36730769	8	~1983
2295743	4591487	7	~1981
2295763	91830521	8	~1984
2295803	4591607	7	~1981
2295841	36733457	8	~1983
2295859	330603697	9	~1985
2295911	4591823	7	~1981
2295913	13775479	8	~1982
2296163	4592327	7	~1981
2296213	13777279	8	~1982
2296271	4592543	7	~1981
2296271	59703047	8
2296367	41334607	8	~1983
2296691	151581607	9	~1984
2296733	252640631	9	~1985
2296817	13780903	8	~1982
2296913	55125913	8	~1983
2296979	4593959	7	~1981

Exp.	Prime Factor	Digits	Year
2297027	225108647	9	~1985
2297039	18376313	8	~1982
2297153	32160143	8	~1983
2297231	4594463	7	~1981
2297311	36756977	8	~1983
2297369	73515809	8	~1984
2297371	36757937	8	~1983
2297411	4594823	7	~1981
2297591	4595183	7	~1981
2297591	18380729	8
2298041	18384329	8	~1982
2298071	4596143	7	~1981
2298089	275770681	9	~1985
2298143	4596287	7	~1981
2298161	68944831	8	~1984
2298203	4596407	7	~1981
2298211	22982111	8	~1982
2298503	4597007	7	~1981
2298577	36777233	8	~1983
2298683	4597367	7	~1981
2298839	4597679	7	~1981
2298953	68968591	8	~1984
2298973	13793839	8	~1982
2299079	4598159	7	~1981
2299147	22991471	8	~1982

Exp.	Prime Factor	Digits	Year
2299259	18394073	8	~1982
2299313	32190383	8	~1983
2299357	13796143	8	~1982
2299387	22993871	8	~1982
2299499	4598999	7	~1981
2299523	73584737	8	~1984
2299727	41395087	8	~1983
2299727	317362327	9
2299733	73591457	8	~1984
2299763	4599527	7	~1981
2299951	22999511	8	~1982
2300003	4600007	7	~1981
2300003	73600097	8
2300017	13800103	8	~1982
2300131	36802097	8	~1983
2300239	23002391	8	~1982
2300377	13802263	8	~1982
2300399	55209577	8	~1983
2300513	13803079	8	~1982
2300513	289864639	9
2300611	23006111	8	~1982
2301029	18408233	8	~1982
2301119	4602239	7	~1981
2301119	18408953	8
2301199	23011991	8	~1982

4.724.182 digits

25-04-13