Small Mersenne Prime Factors (page 760/5670)

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
5682701	45461609	8	~1985
5682779	11365559	8	~1984
5682841	34097047	8	~1985
5682899	11365799	8	~1984
5683037	34098223	8	~1985
5683081	34098487	8	~1985
5683283	11366567	8	~1984
5683319	11366639	8	~1984
5683343	11366687	8	~1984
5683421	45467369	8	~1985
5683471	56834711	8	~1985
5683841	45470729	8	~1985
5683949	136414777	9	~1986
5683961	34103767	8	~1985
5684071	102313279	9	~1986
5684083	56840831	8	~1985
5684099	11368199	8	~1984
5684183	11368367	8	~1984
5684257	34105543	8	~1985
5684411	11368823	8	~1984
5684533	90952529	8	~1986
5684641	34107847	8	~1985
5684669	45477353	8	~1985
5684699	11369399	8	~1984
5684927	102328687	9	~1986

Exp.	Prime Factor	Digits	Year
5685241	90963857	8	~1986
5685371	11370743	8	~1984
5685677	45485417	8	~1985
5685739	56857391	8	~1985
5685863	11371727	8	~1984
5685961	125091143	9	~1986
5686181	34117087	8	~1985
5686403	11372807	8	~1984
5686591	90985457	8	~1986
5686601	45492809	8	~1985
5686691	45493529	8	~1985
5686777	170603311	9	~1987
5686931	921282823	9	~1988
5687053	90992849	8	~1986
5687179	56871791	8	~1985
5687191	102369439	9	~1986
5687239	56872391	8	~1985
5687261	34123567	8	~1985
5687471	11374943	8	~1984
5687501	45500009	8	~1985
5687687	45501497	8	~1985
5687791	56877911	8	~1985
5687999	238895959	9	~1987
5688037	34128223	8	~1985
5688071	11376143	8	~1984

Exp.	Prime Factor	Digits	Year
5688329	216156503	9	~1987
5688359	11376719	8	~1984
5688503	11377007	8	~1984
5688911	11377823	8	~1984
5688983	11377967	8	~1984
5689091	45512729	8	~1985
5689241	34135447	8	~1985
5689643	11379287	8	~1984
5689793	34138759	8	~1985
5689811	11379623	8	~1984
5689813	136555513	9	~1986
5690057	34140343	8	~1985
5690213	34141279	8	~1985
5690339	11380679	8	~1984
5690473	91047569	8	~1986
5690561	45524489	8	~1985
5690651	11381303	8	~1984
5690669	307296127	9	~1987
5690717	79670039	8	~1986
5690827	102434887	9	~1986
5690987	45527897	8	~1985
5691043	56910431	8	~1985
5691083	11382167	8	~1984
5691137	45529097	8	~1985
5691359	11382719	8	~1984

Exp.	Prime Factor	Digits	Year
5691463	56914631	8	~1985
5691479	45531833	8	~1985
5691691	56916911	8	~1985
5691827	45534617	8	~1985
5691913	34151479	8	~1985
5692133	136611193	9	~1986
5692279	56922791	8	~1985
5692391	11384783	8	~1984
5692559	11385119	8	~1984
5692763	11385527	8	~1984
5692811	11385623	8	~1984
5692853	34157119	8	~1985
5693123	11386247	8	~1984
5693357	717362983	9	~1988
5693399	11386799	8	~1984
5693461	34160767	8	~1985
5693539	56935391	8	~1985
5693543	11387087	8	~1984
5693591	11387183	8	~1984
5693621	216357599	9	~1987
5693899	102490183	9	~1986
5693921	34163527	8	~1985
5694011	11388023	8	~1984
5694431	11388863	8	~1984
5694431	45555449	8

5.366.787 digits

26-02-08