Small Mersenne Prime Factors (page 722/5025)

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
5564879	11129759	8	~1984
5565023	11130047	8	~1984
5565083	11130167	8	~1984
5565257	33391543	8	~1985
5565257	44522057	8
5565473	33392839	8	~1985
5565697	166970911	9	~1987
5565713	33394279	8	~1985
5565809	44526473	8	~1985
5565827	44526617	8	~1985
5565887	768092407	9	~1988
5566091	11132183	8	~1984
5566097	133586329	9	~1986
5566147	55661471	8	~1985
5566271	11132543	8	~1984
5566441	33398647	8	~1985
5566501	33399007	8	~1985
5566523	11133047	8	~1984
5566553	33399319	8	~1985
5566559	11133119	8	~1984
5566567	89065073	8	~1986
5566901	44535209	8	~1985
5566919	11133839	8	~1984
5566969	122473319	9	~1986
5567033	33402199	8	~1985

Exp.	Prime Factor	Digits	Year
5567183	144746759	9	~1986
5567533	89080529	8	~1986
5567801	44542409	8	~1985
5567843	11135687	8	~1984
5567873	33407239	8	~1985
5567987	44543897	8	~1985
5568149	77954087	8	~1986
5568161	44545289	8	~1985
5568239	44545913	8	~1985
5568547	55685471	8	~1985
5568677	33412063	8	~1985
5568791	11137583	8	~1984
5568821	33412927	8	~1985
5568847	100239247	9	~1986
5568971	44551769	8	~1985
5569079	11138159	8	~1984
5569163	11138327	8	~1984
5569211	11138423	8	~1984
5569271	144801047	9	~1986
5569379	11138759	8	~1984
5569441	122527703	9	~1986
5569517	33417103	8	~1985
5569589	44556713	8	~1985
5569997	33419983	8	~1985
5570039	11140079	8	~1984

Exp.	Prime Factor	Digits	Year
5570267	44562137	8	~1985
5570269	133686457	9	~1986
5570303	11140607	8	~1984
5570501	33423007	8	~1985
5570633	33423799	8	~1985
5570699	11141399	8	~1984
5570723	11141447	8	~1984
5570833	33424999	8	~1985
5570879	11141759	8	~1984
5571179	11142359	8	~1984
5571353	33428119	8	~1985
5571487	55714871	8	~1985
5571491	11142983	8	~1984
5571539	11143079	8	~1984
5571763	55717631	8	~1985
5572097	78009359	8	~1986
5572297	33433783	8	~1985
5572313	78012383	8	~1986
5572331	11144663	8	~1984
5572439	11144879	8	~1984
5572571	11145143	8	~1984
5572631	11145263	8	~1984
5572751	11145503	8	~1984
5572793	33436759	8	~1985
5572907	44583257	8	~1985

Exp.	Prime Factor	Digits	Year
5572907	100312327	9
5573257	33439543	8	~1985
5573363	11146727	8	~1984
5573461	33440767	8	~1985
5573587	55735871	8	~1985
5573677	33442063	8	~1985
5573723	11147447	8	~1984
5573993	167219791	9	~1987
5574083	178370657	9	~1987
5574313	33445879	8	~1985
5574367	55743671	8	~1985
5574427	89190833	8	~1986
5574977	44599817	8	~1985
5575019	11150039	8	~1984
5575259	11150519	8	~1984
5575399	55753991	8	~1985
5575561	33453367	8	~1985
5575693	33454159	8	~1985
5575783	758306489	9	~1988
5576047	100368847	9	~1986
5576099	11152199	8	~1984
5576303	11152607	8	~1984
5576371	55763711	8	~1985
5576413	33458479	8	~1985
5576537	44612297	8	~1985

4.724.182 digits

25-04-13