Small Mersenne Prime Factors (page 873/5610)

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
7214843	14429687	8	~1985
7214917	43289503	8	~1986
7214951	360747551	9	~1988
7215127	72151271	8	~1986
7215223	72152231	8	~1986
7215449	57723593	8	~1986
7215547	72155471	8	~1986
7215553	43293319	8	~1986
7216091	57728729	8	~1986
7216199	14432399	8	~1985
7216213	43297279	8	~1986
7216247	129892447	9	~1987
7216343	14432687	8	~1985
7216439	14432879	8	~1985
7216787	57734297	8	~1986
7216987	115471793	9	~1987
7217279	14434559	8	~1985
7217407	72174071	8	~1986
7217657	43305943	8	~1986
7217731	303144703	9	~1988
7217747	173225929	9	~1987
7217753	43306519	8	~1986
7217939	14435879	8	~1985
7218053	43308319	8	~1986
7218181	43309087	8	~1986

Exp.	Prime Factor	Digits	Year
7218269	57746153	8	~1986
7218433	43310599	8	~1986
7218637	43311823	8	~1986
7218929	274319303	9	~1988
7219139	14438279	8	~1985
7219391	14438783	8	~1985
7219483	72194831	8	~1986
7219519	72195191	8	~1986
7219703	14439407	8	~1985
7219871	57758969	8	~1986
7220407	72204071	8	~1986
7220483	14440967	8	~1985
7220711	14441423	8	~1985
7220933	43325599	8	~1986
7221013	43326079	8	~1986
7221299	14442599	8	~1985
7221301	43327807	8	~1986
7221587	57772697	8	~1986
7221757	43330543	8	~1986
7221871	72218711	8	~1986
7221917	43331503	8	~1986
7222199	57777593	8	~1986
7222199	173332777	9
7222661	1487868167	10	~1989
7222723	72227231	8	~1986

Exp.	Prime Factor	Digits	Year
7222811	231129953	9	~1988
7222991	14445983	8	~1985
7223033	43338199	8	~1986
7223039	14446079	8	~1985
7223053	43338319	8	~1986
7223123	14446247	8	~1985
7223519	14447039	8	~1985
7223683	72236831	8	~1986
7223981	57791849	8	~1986
7223999	173375977	9	~1987
7224029	57792233	8	~1986
7224131	361206551	9	~1988
7224211	72242111	8	~1986
7224341	43346047	8	~1986
7224359	14448719	8	~1985
7224517	43347103	8	~1986
7224551	14449103	8	~1985
7225019	14450039	8	~1985
7225271	14450543	8	~1985
7225441	115607057	9	~1987
7225531	115608497	9	~1987
7225811	14451623	8	~1985
7225931	14451863	8	~1985
7226111	14452223	8	~1985
7226183	14452367	8	~1985

Exp.	Prime Factor	Digits	Year
7226333	43357999	8	~1986
7226369	57810953	8	~1986
7226641	43359847	8	~1986
7226909	1951265431	10	~1990
7227013	43362079	8	~1986
7227967	72279671	8	~1986
7228093	159018047	9	~1987
7228211	14456423	8	~1985
7228483	72284831	8	~1986
7228631	14457263	8	~1985
7228691	14457383	8	~1985
7228703	14457407	8	~1985
7228811	57830489	8	~1986
7228913	43373479	8	~1986
7228943	14457887	8	~1985
7228979	14457959	8	~1985
7228981	43373887	8	~1986
7229011	72290111	8	~1986
7229219	14458439	8	~1985
7229581	43377487	8	~1986
7229857	43379143	8	~1986
7229951	14459903	8	~1985
7230071	14460143	8	~1985
7230131	14460263	8	~1985
7230131	130142359	9

5.307.017 digits

26-01-11