Small Mersenne Prime Factors (page 963/5340)

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
8774543	17549087	8	~1985
8774693	52648159	8	~1986
8774917	52649503	8	~1986
8774939	17549879	8	~1985
8775457	140407313	9	~1987
8775659	17551319	8	~1985
8775979	421246993	9	~1989
8775997	52655983	8	~1986
8776291	87762911	8	~1987
8776387	157974967	9	~1988
8776541	52659247	8	~1986
8776633	140426129	9	~1987
8776693	52660159	8	~1986
8776697	52660183	8	~1986
8776739	17553479	8	~1985
8776753	52660519	8	~1986
8777033	52662199	8	~1986
8777243	17554487	8	~1985
8777519	17555039	8	~1985
8777819	70222553	8	~1987
8777837	70222697	8	~1987
8778023	17556047	8	~1985
8778557	491599193	9	~1989
8778569	474042727	9	~1989
8778593	263357791	9	~1988

Exp.	Prime Factor	Digits	Year
8778899	70231193	8	~1987
8779481	52676887	8	~1986
8779621	52677727	8	~1986
8780113	52680679	8	~1986
8780171	17560343	8	~1985
8780459	17560919	8	~1985
8780543	17561087	8	~1985
8780677	52684063	8	~1986
8781013	52686079	8	~1986
8781181	52687087	8	~1986
8781449	122940287	9	~1987
8781491	17562983	8	~1985
8781497	52688983	8	~1986
8781659	17563319	8	~1985
8781683	17563367	8	~1985
8781683	228323759	9
8781937	52691623	8	~1986
8781953	52691719	8	~1986
8783009	122962127	9	~1987
8783017	52698103	8	~1986
8783147	70265177	8	~1987
8783161	52698967	8	~1986
8783239	87832391	8	~1987
8783771	70270169	8	~1987
8783843	17567687	8	~1985

Exp.	Prime Factor	Digits	Year
8783903	17567807	8	~1985
8784731	17569463	8	~1985
8784757	52708543	8	~1986
8784983	17569967	8	~1985
8785177	52711063	8	~1986
8785223	17570447	8	~1985
8785397	70283177	8	~1987
8785519	210852457	9	~1988
8786171	17572343	8	~1985
8786611	87866111	8	~1987
8786831	158162959	9	~1988
8786957	70295657	8	~1987
8787431	17574863	8	~1985
8787491	17574983	8	~1985
8787503	17575007	8	~1985
8787749	210905977	9	~1988
8787809	123029327	9	~1987
8787811	158180599	9	~1988
8787893	52727359	8	~1986
8787979	87879791	8	~1987
8788037	52728223	8	~1986
8788477	52730863	8	~1986
8788523	17577047	8	~1985
8788957	52733743	8	~1986
8789041	52734247	8	~1986

Exp.	Prime Factor	Digits	Year
8789057	52734343	8	~1986
8789279	17578559	8	~1985
8789579	70316633	8	~1987
8789843	17579687	8	~1985
8789939	17579879	8	~1985
8789999	17579999	8	~1985
8790413	52742479	8	~1986
8790473	52742839	8	~1986
8790557	210973369	9	~1988
8790599	17581199	8	~1985
8790839	17581679	8	~1985
8791283	17582567	8	~1985
8791297	140660753	9	~1987
8791477	52748863	8	~1986
8791571	17583143	8	~1985
8791801	52750807	8	~1986
8791933	52751599	8	~1986
8792039	17584079	8	~1985
8792059	211009417	9	~1988
8792099	17584199	8	~1985
8792099	70336793	8
8792123	17584247	8	~1985
8792293	52753759	8	~1986
8792351	17584703	8	~1985
8792401	52754407	8	~1986

5.037.460 digits

25-09-07