Small Mersenne Prime Factors (page 939/5610)

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
8185421	49112527	8	~1986
8185451	16370903	8	~1985
8185649	65485193	8	~1986
8185657	49113943	8	~1986
8185799	16371599	8	~1985
8185981	49115887	8	~1986
8186099	16372199	8	~1985
8186219	16372439	8	~1985
8186351	16372703	8	~1985
8186411	16372823	8	~1985
8186603	16373207	8	~1985
8186621	49119727	8	~1986
8186831	16373663	8	~1985
8186861	49121167	8	~1986
8186933	49121599	8	~1986
8187031	81870311	8	~1987
8187089	65496713	8	~1986
8187197	65497577	8	~1986
8187337	1031604463	10	~1989
8187373	49124239	8	~1986
8187539	65500313	8	~1986
8187719	16375439	8	~1985
8187719	65501753	8
8187743	16375487	8	~1985
8188163	262021217	9	~1988

Exp.	Prime Factor	Digits	Year
8188547	147393847	9	~1987
8188613	49131679	8	~1986
8188693	180151247	9	~1988
8189227	147406087	9	~1987
8189453	49136719	8	~1986
8189593	49137559	8	~1986
8189663	16379327	8	~1985
8189681	49138087	8	~1986
8189777	65518217	8	~1986
8189939	16379879	8	~1985
8189963	16379927	8	~1985
8189981	49139887	8	~1986
8189999	16379999	8	~1985
8190029	65520233	8	~1986
8190097	49140583	8	~1986
8190131	16380263	8	~1985
8190359	16380719	8	~1985
8190761	65526089	8	~1986
8191283	16382567	8	~1985
8191307	65530457	8	~1986
8191321	131061137	9	~1987
8191493	49148959	8	~1986
8191613	196598713	9	~1988
8191633	49149799	8	~1986
8192039	16384079	8	~1985

Exp.	Prime Factor	Digits	Year
8192081	262146593	9	~1988
8192111	16384223	8	~1985
8192423	16384847	8	~1985
8192441	49154647	8	~1986
8192533	245775991	9	~1988
8192813	49156879	8	~1986
8192881	49157287	8	~1986
8192887	81928871	8	~1987
8193001	49158007	8	~1986
8193041	49158247	8	~1986
8193253	49159519	8	~1986
8193551	16387103	8	~1985
8193571	131097137	9	~1987
8193599	16387199	8	~1985
8193667	81936671	8	~1987
8193791	16387583	8	~1985
8193803	16387607	8	~1985
8193851	16387703	8	~1985
8193929	65551433	8	~1986
8193961	49163767	8	~1986
8194127	65553017	8	~1986
8194217	65553737	8	~1986
8194457	49166743	8	~1986
8194481	65555849	8	~1986
8194583	16389167	8	~1985

Exp.	Prime Factor	Digits	Year
8194691	16389383	8	~1985
8195021	65560169	8	~1986
8195111	65560889	8	~1986
8195303	16390607	8	~1985
8195399	16390799	8	~1985
8195617	196694809	9	~1988
8195651	16391303	8	~1985
8195699	16391399	8	~1985
8195711	16391423	8	~1985
8196113	49176679	8	~1986
8196469	327858761	9	~1988
8196491	16392983	8	~1985
8196523	81965231	8	~1987
8196563	16393127	8	~1985
8196577	49179463	8	~1986
8196599	16393199	8	~1985
8196827	65574617	8	~1986
8197823	16395647	8	~1985
8197921	49187527	8	~1986
8198009	114772127	9	~1987
8198459	147572263	9	~1987
8198639	16397279	8	~1985
8198717	49192303	8	~1986
8198759	16397519	8	~1985
8198759	65590073	8

5.307.017 digits

26-01-11