Small Mersenne Prime Factors (page 699/5535)

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
4996457	69950399	8	~1985
4996553	69951743	8	~1985
4996559	9993119	7	~1983
4996619	9993239	7	~1983
4996627	49966271	8	~1985
4996637	39973097	8	~1985
4996679	9993359	7	~1983
4996697	29980183	8	~1984
4996703	9993407	7	~1983
4996709	39973673	8	~1985
4996723	49967231	8	~1985
4996757	29980543	8	~1984
4997471	39979769	8	~1985
4997533	29985199	8	~1984
4997981	29987887	8	~1984
4998113	69973583	8	~1985
4998131	9996263	7	~1983
4998211	49982111	8	~1985
4998229	109961039	9	~1986
4998341	29990047	8	~1984
4998359	9996719	7	~1983
4998647	39989177	8	~1985
4998673	149960191	9	~1986
4998683	9997367	7	~1983
4999103	9998207	7	~1983

Exp.	Prime Factor	Digits	Year
4999307	39994457	8	~1985
4999447	49994471	8	~1985
4999523	9999047	7	~1983
4999823	119995753	9	~1986
5000111	10000223	8	~1983
5000161	30000967	8	~1984
5000311	50003111	8	~1985
5000399	10000799	8	~1983
5000423	120010153	9	~1986
5000701	30004207	8	~1984
5000759	40006073	8	~1985
5000783	10001567	8	~1983
5000861	30005167	8	~1984
5000903	10001807	8	~1983
5000977	30005863	8	~1984
5001167	40009337	8	~1985
5001197	40009577	8	~1985
5001203	10002407	8	~1983
5001299	10002599	8	~1983
5001413	30008479	8	~1984
5001443	10002887	8	~1983
5001593	280089209	9	~1987
5001779	10003559	8	~1983
5002103	10004207	8	~1983
5002223	10004447	8	~1983

Exp.	Prime Factor	Digits	Year
5002273	30013639	8	~1984
5002331	10004663	8	~1983
5002463	120059113	9	~1986
5002553	120061273	9	~1986
5002579	50025791	8	~1985
5002583	10005167	8	~1983
5003191	50031911	8	~1985
5003227	50032271	8	~1985
5003231	10006463	8	~1983
5003309	1000661801	10	~1988
5003543	10007087	8	~1983
5003549	70049687	8	~1985
5003591	10007183	8	~1983
5003711	10007423	8	~1983
5003893	80062289	8	~1986
5003923	120094153	9	~1986
5004367	50043671	8	~1985
5004491	10008983	8	~1983
5004539	10009079	8	~1983
5004821	40038569	8	~1985
5004841	30029047	8	~1984
5004859	50048591	8	~1985
5004929	70069007	8	~1985
5004941	30029647	8	~1984
5005223	10010447	8	~1983

Exp.	Prime Factor	Digits	Year
5005289	40042313	8	~1985
5005621	1231382767	10	~1988
5005669	150170071	9	~1986
5005909	270319087	9	~1987
5005921	80094737	8	~1986
5006081	40048649	8	~1985
5006153	70086143	8	~1985
5006237	40049897	8	~1985
5006399	10012799	8	~1983
5006503	80104049	8	~1986
5006509	560729009	9	~1988
5006537	30039223	8	~1984
5006623	80105969	8	~1986
5006657	30039943	8	~1984
5006657	40053257	8
5006773	30040639	8	~1984
5006923	50069231	8	~1985
5007181	30043087	8	~1984
5007539	10015079	8	~1983
5007593	510774487	9	~1987
5007719	40061753	8	~1985
5007841	30047047	8	~1984
5008187	90147367	8	~1986
5008739	10017479	8	~1983
5008841	40070729	8	~1985

5.232.152 digits

25-12-07