Small Mersenne Prime Factors (page 712/5730)

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
5068213	30409279	8	~1985
5068319	10136639	8	~1983
5068523	10137047	8	~1983
5068559	10137119	8	~1983
5068781	364952233	9	~1987
5068859	10137719	8	~1983
5068957	152068711	9	~1986
5069063	10138127	8	~1983
5069231	10138463	8	~1983
5069633	70974863	8	~1985
5069639	10139279	8	~1983
5069681	40557449	8	~1985
5070007	50700071	8	~1985
5070433	365071177	9	~1987
5070497	40563977	8	~1985
5070497	70986959	8
5070521	40564169	8	~1985
5070599	10141199	8	~1983
5070599	40564793	8
5070643	50706431	8	~1985
5070671	10141343	8	~1983
5070959	40567673	8	~1985
5071103	10142207	8	~1983
5071177	81138833	8	~1986
5071343	10142687	8	~1983

Exp.	Prime Factor	Digits	Year
5071351	50713511	8	~1985
5071361	40570889	8	~1985
5071471	50714711	8	~1985
5071511	91287199	8	~1986
5071751	10143503	8	~1983
5071883	10143767	8	~1983
5071919	10143839	8	~1983
5071931	10143863	8	~1983
5072531	10145063	8	~1983
5072707	91308727	8	~1986
5072863	50728631	8	~1985
5072993	30437959	8	~1985
5073017	30438103	8	~1985
5073241	30439447	8	~1985
5073371	10146743	8	~1983
5073457	30440743	8	~1985
5073493	30440959	8	~1985
5073559	202942361	9	~1987
5073689	71031647	8	~1985
5073821	30442927	8	~1985
5073851	10147703	8	~1983
5073923	10147847	8	~1983
5074081	30444487	8	~1985
5074103	10148207	8	~1983
5074151	40593209	8	~1985

Exp.	Prime Factor	Digits	Year
5074337	71040719	8	~1985
5074373	30446239	8	~1985
5074451	253722551	9	~1987
5074571	10149143	8	~1983
5074633	81194129	8	~1986
5074709	40597673	8	~1985
5074747	50747471	8	~1985
5074801	30448807	8	~1985
5074841	40598729	8	~1985
5074847	91347247	8	~1986
5074859	10149719	8	~1983
5074967	91349407	8	~1986
5075143	50751431	8	~1985
5075207	1258651337	10	~1988
5075237	30451423	8	~1985
5075519	10151039	8	~1983
5075579	40604633	8	~1985
5075879	10151759	8	~1983
5075951	10151903	8	~1983
5076053	30456319	8	~1985
5076161	30456967	8	~1985
5076179	40609433	8	~1985
5076221	40609769	8	~1985
5076473	30458839	8	~1985
5076503	10153007	8	~1983

Exp.	Prime Factor	Digits	Year
5076551	40612409	8	~1985
5076569	71071967	8	~1985
5076569	152297071	9
5076671	10153343	8	~1983
5076719	10153439	8	~1983
5076853	111690767	9	~1986
5076913	30461479	8	~1985
5076983	10153967	8	~1983
5077283	10154567	8	~1983
5077759	50777591	8	~1985
5077931	10155863	8	~1983
5078123	10156247	8	~1983
5078167	50781671	8	~1985
5078243	3331327409	10	~1990
5078663	10157327	8	~1983
5078743	50787431	8	~1985
5078851	81261617	8	~1986
5078939	10157879	8	~1983
5079059	91423063	8	~1986
5079059	121897417	9
5079079	50790791	8	~1985
5079083	10158167	8	~1983
5079097	30474583	8	~1985
5079233	71109263	8	~1985
5079359	10158719	8	~1983

5.426.516 digits

26-03-08