Small Mersenne Prime Factors (page 889/5205)

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
7771481	46628887	8	~1986
7771619	62172953	8	~1986
7771661	46629967	8	~1986
7771661	62173289	8
7771859	15543719	8	~1985
7772189	62177513	8	~1986
7772341	46634047	8	~1986
7772353	186536473	9	~1987
7772393	186537433	9	~1987
7772507	62180057	8	~1986
7772543	15545087	8	~1985
7772641	46635847	8	~1986
7772753	46636519	8	~1986
7772797	186547129	9	~1987
7772879	15545759	8	~1985
7773053	108822743	9	~1987
7773119	15546239	8	~1985
7773173	46639039	8	~1986
7773179	15546359	8	~1985
7773179	62185433	8
7773431	15546863	8	~1985
7773449	108828287	9	~1987
7773481	46640887	8	~1986
7773611	15547223	8	~1985
7773617	46641703	8	~1986

Exp.	Prime Factor	Digits	Year
7773617	62188937	8
7773803	15547607	8	~1985
7773877	46643263	8	~1986
7773917	46643503	8	~1986
7773929	62191433	8	~1986
7774601	46647607	8	~1986
7774651	77746511	8	~1987
7774751	15549503	8	~1985
7774979	15549959	8	~1985
7775039	15550079	8	~1985
7775051	15550103	8	~1985
7775099	62200793	8	~1986
7775231	15550463	8	~1985
7775279	15550559	8	~1985
7775459	15550919	8	~1985
7775543	15551087	8	~1985
7775597	62204777	8	~1986
7775717	46654303	8	~1986
7775843	15551687	8	~1985
7775879	15551759	8	~1985
7776143	15552287	8	~1985
7776383	15552767	8	~1985
7776649	186639577	9	~1987
7777223	15554447	8	~1985
7777291	124436657	9	~1987

Exp.	Prime Factor	Digits	Year
7777421	62219369	8	~1986
7777499	15554999	8	~1985
7777843	77778431	8	~1987
7778159	15556319	8	~1985
7778279	15556559	8	~1985
7778591	15557183	8	~1985
7778647	124458353	9	~1987
7778759	15557519	8	~1985
7778801	62230409	8	~1986
7778941	124463057	9	~1987
7779077	62232617	8	~1986
7779137	62233097	8	~1986
7779203	15558407	8	~1985
7779713	46678279	8	~1986
7779787	77797871	8	~1987
7779847	77798471	8	~1987
7780343	15560687	8	~1985
7780351	124485617	9	~1987
7780523	15561047	8	~1985
7780691	62245529	8	~1986
7780711	140052799	9	~1987
7780757	62246057	8	~1986
7780891	77808911	8	~1987
7780919	15561839	8	~1985
7781159	15562319	8	~1985

Exp.	Prime Factor	Digits	Year
7781261	46687567	8	~1986
7781297	46687783	8	~1986
7781573	46689439	8	~1986
7781591	15563183	8	~1985
7781821	46690927	8	~1986
7782377	62259017	8	~1986
7782587	62260697	8	~1986
7782779	15565559	8	~1985
7782917	46697503	8	~1986
7783343	15566687	8	~1985
7783621	46701727	8	~1986
7783757	62270057	8	~1986
7784039	186816937	9	~1987
7784221	171252863	9	~1987
7784459	15568919	8	~1985
7784593	46707559	8	~1986
7784723	15569447	8	~1985
7784729	233541871	9	~1988
7784771	62278169	8	~1986
7784831	15569663	8	~1985
7784951	15569903	8	~1985
7784981	233549431	9	~1988
7785131	15570263	8	~1985
7785341	46712047	8	~1986
7785359	15570719	8	~1985

4.903.097 digits

25-07-08