Small Mersenne Prime Factors (page 996/5610)

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
9037313	54223879	8	~1986
9037451	72299609	8	~1987
9037499	18074999	8	~1985
9037499	72299993	8
9037601	54225607	8	~1986
9037667	72301337	8	~1987
9037681	54226087	8	~1986
9037751	18075503	8	~1985
9037811	18075623	8	~1985
9037991	72303929	8	~1987
9038189	433833073	9	~1989
9038219	18076439	8	~1985
9038273	54229639	8	~1986
9038507	72308057	8	~1987
9038723	18077447	8	~1985
9038831	18077663	8	~1985
9038857	54233143	8	~1986
9038867	216932809	9	~1988
9039143	18078287	8	~1985
9039323	18078647	8	~1985
9039959	72319673	8	~1987
9039983	18079967	8	~1985
9040477	54242863	8	~1986
9040517	126567239	9	~1987
9040573	54243439	8	~1986

Exp.	Prime Factor	Digits	Year
9040949	126573287	9	~1987
9041497	54248983	8	~1986
9041693	54250159	8	~1986
9041759	18083519	8	~1985
9041941	54251647	8	~1986
9041953	54251719	8	~1986
9042221	54253327	8	~1986
9042223	578702273	9	~1989
9042713	217025113	9	~1988
9042779	18085559	8	~1985
9042797	72342377	8	~1987
9042877	54257263	8	~1986
9043081	54258487	8	~1986
9043121	72344969	8	~1987
9043271	18086543	8	~1985
9043421	72347369	8	~1987
9043513	54261079	8	~1986
9043571	72348569	8	~1987
9043591	90435911	8	~1987
9043823	18087647	8	~1985
9043871	18087743	8	~1985
9043997	72351977	8	~1987
9044159	18088319	8	~1985
9044303	18088607	8	~1985
9044471	18088943	8	~1985

Exp.	Prime Factor	Digits	Year
9044771	18089543	8	~1985
9044807	72358457	8	~1987
9044837	54269023	8	~1986
9044837	72358697	8
9045017	126630239	9	~1987
9045073	54270439	8	~1986
9045677	54274063	8	~1986
9045779	18091559	8	~1985
9045809	72366473	8	~1987
9045823	90458231	8	~1987
9045913	54275479	8	~1986
9045977	72367817	8	~1987
9045983	18091967	8	~1985
9046001	54276007	8	~1986
9046031	72368249	8	~1987
9046151	18092303	8	~1985
9046733	54280399	8	~1986
9046841	54281047	8	~1986
9047041	54282247	8	~1986
9047321	54283927	8	~1986
9047393	54284359	8	~1986
9047399	18094799	8	~1985
9047627	72381017	8	~1987
9047639	18095279	8	~1985
9048491	18096983	8	~1985

Exp.	Prime Factor	Digits	Year
9048703	90487031	8	~1987
9048937	54293623	8	~1986
9049121	54294727	8	~1986
9049211	72393689	8	~1987
9049259	18098519	8	~1985
9049583	18099167	8	~1985
9049811	72398489	8	~1987
9050183	18100367	8	~1985
9050191	380108023	9	~1989
9050221	54301327	8	~1986
9050563	90505631	8	~1987
9050663	18101327	8	~1985
9050939	18101879	8	~1985
9051047	72408377	8	~1987
9051061	144816977	9	~1988
9051071	18102143	8	~1985
9051269	72410153	8	~1987
9051313	54307879	8	~1986
9051323	18102647	8	~1985
9051437	72411497	8	~1987
9051737	54310423	8	~1987
9051863	18103727	8	~1985
9051929	72415433	8	~1987
9051989	126727847	9	~1987
9052033	54312199	8	~1987

5.307.017 digits

26-01-11