Small Mersenne Prime Factors (page 527/5775)

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
3106307	24850457	8	~1983
3106319	74551657	8	~1984
3106381	49702097	8	~1984
3106381	93191431	8
3106429	68341439	8	~1984
3106643	6213287	7	~1982
3106703	6213407	7	~1982
3106751	6213503	7	~1982
3106777	49708433	8	~1984
3106849	571660217	9	~1987
3106919	6213839	7	~1982
3107033	18642199	8	~1983
3107081	24856649	8	~1983
3107171	24857369	8	~1983
3107249	24857993	8	~1983
3107483	372897961	9	~1986
3107633	18645799	8	~1983
3107711	6215423	7	~1982
3107827	49725233	8	~1984
3107893	18647359	8	~1983
3107927	74590249	8	~1984
3108019	74592457	8	~1984
3108023	6216047	7	~1982
3108067	55945207	8	~1984
3108239	6216479	7	~1982

Exp.	Prime Factor	Digits	Year
3108239	55948303	8
3108359	6216719	7	~1982
3108359	24866873	8
3108373	18650239	8	~1983
3108461	18650767	8	~1983
3108551	6217103	7	~1982
3108737	93262111	8	~1985
3108779	24870233	8	~1983
3108893	18653359	8	~1983
3109031	24872249	8	~1983
3109069	93272071	8	~1985
3109091	80836367	8	~1984
3109159	31091591	8	~1983
3109193	18655159	8	~1983
3109307	149246737	9	~1985
3109333	18655999	8	~1983
3109333	68405327	8
3109343	6218687	7	~1982
3109349	43530887	8	~1984
3109397	18656383	8	~1983
3109411	31094111	8	~1983
3109441	18656647	8	~1983
3109619	24876953	8	~1983
3109751	6219503	7	~1982
3109817	18658903	8	~1983

Exp.	Prime Factor	Digits	Year
3109837	18659023	8	~1983
3109921	18659527	8	~1983
3110231	6220463	7	~1982
3110299	31102991	8	~1983
3110321	24882569	8	~1983
3110377	18662263	8	~1983
3110593	74654233	8	~1984
3110621	18663727	8	~1983
3110689	93320671	8	~1985
3110741	192865943	9	~1985
3110771	6221543	7	~1982
3110963	6221927	7	~1982
3111131	6222263	7	~1982
3111397	18668383	8	~1983
3111431	248914481	9	~1986
3111481	49783697	8	~1984
3111659	6223319	7	~1982
3111863	6223727	7	~1982
3112271	24898169	8	~1983
3112399	56023183	8	~1984
3112471	31124711	8	~1983
3112687	31126871	8	~1983
3112687	74704489	8
3112721	24901769	8	~1983
3112859	6225719	7	~1982

Exp.	Prime Factor	Digits	Year
3112919	6225839	7	~1982
3112933	68484527	8	~1984
3112973	18677839	8	~1983
3112973	43581623	8
3113053	168104863	9	~1985
3113101	18678607	8	~1983
3113111	5286062479	10	~1989
3113399	6226799	7	~1982
3113447	24907577	8	~1983
3113471	56042479	8	~1984
3113707	199277249	9	~1985
3113783	6227567	7	~1982
3113821	49821137	8	~1984
3113833	49821329	8	~1984
3113899	74733577	8	~1984
3113939	56050903	8	~1984
3113963	6227927	7	~1982
3114211	49827377	8	~1984
3114283	31142831	8	~1983
3114359	56058463	8	~1984
3114437	24915497	8	~1983
3114497	24915977	8	~1983
3114719	6229439	7	~1982
3114889	68527559	8	~1984
3114889	242961343	9

5.471.290 digits

26-03-29