Small Mersenne Prime Factors (page 858/5085)

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
7405757	44434543	8	~1986
7406041	44436247	8	~1986
7406099	14812199	8	~1985
7406111	14812223	8	~1985
7406297	103688159	9	~1987
7406309	59250473	8	~1986
7406351	14812703	8	~1985
7406579	14813159	8	~1985
7406603	14813207	8	~1985
7406807	59254457	8	~1986
7406957	59255657	8	~1986
7406963	14813927	8	~1985
7407097	44442583	8	~1986
7407299	59258393	8	~1986
7407611	14815223	8	~1985
7407637	44445823	8	~1986
7407761	59262089	8	~1986
7408087	74080871	8	~1986
7408241	59265929	8	~1986
7408301	44449807	8	~1986
7408301	59266409	8
7408649	103721087	9	~1987
7408813	44452879	8	~1986
7408853	44453119	8	~1986
7408883	14817767	8	~1985

Exp.	Prime Factor	Digits	Year
7409431	74094311	8	~1986
7410187	1897007873	10	~1990
7410191	59281529	8	~1986
7410281	44461687	8	~1986
7410553	44463319	8	~1986
7410569	59284553	8	~1986
7410743	14821487	8	~1985
7410857	44465143	8	~1986
7411399	296455961	9	~1988
7411667	59293337	8	~1986
7411687	74116871	8	~1986
7411823	14823647	8	~1985
7412159	14824319	8	~1985
7412183	14824367	8	~1985
7412341	44474047	8	~1986
7412351	59298809	8	~1986
7412593	44475559	8	~1986
7412653	44475919	8	~1986
7412681	44476087	8	~1986
7412843	14825687	8	~1985
7412857	44477143	8	~1986
7412891	59303129	8	~1986
7412921	44477527	8	~1986
7413053	44478319	8	~1986
7413187	177916489	9	~1987

Exp.	Prime Factor	Digits	Year
7413359	14826719	8	~1985
7413443	14826887	8	~1985
7413641	44481847	8	~1986
7413811	74138111	8	~1986
7413871	74138711	8	~1986
7414037	281733407	9	~1988
7414217	103799039	9	~1987
7414523	14829047	8	~1985
7414613	103804583	9	~1987
7414937	44489623	8	~1986
7415183	14830367	8	~1985
7415257	44491543	8	~1986
7415423	14830847	8	~1985
7415803	74158031	8	~1986
7415839	133485103	9	~1987
7415861	44495167	8	~1986
7415977	44495863	8	~1986
7416191	14832383	8	~1985
7416377	44498263	8	~1986
7416443	14832887	8	~1985
7416869	59334953	8	~1986
7417021	44502127	8	~1986
7417169	59337353	8	~1986
7417357	44504143	8	~1986
7417439	59339513	8	~1986

Exp.	Prime Factor	Digits	Year
7417507	652740617	9	~1989
7417643	14835287	8	~1985
7417643	311541007	9
7417757	59342057	8	~1986
7417829	356055793	9	~1988
7418459	14836919	8	~1985
7418497	222554911	9	~1988
7418501	44511007	8	~1986
7418737	44512423	8	~1986
7419143	14838287	8	~1985
7419337	44516023	8	~1986
7419913	44519479	8	~1986
7420043	14840087	8	~1985
7420243	74202431	8	~1986
7420339	74203391	8	~1986
7420397	44522383	8	~1986
7420519	534277369	9	~1988
7420643	14841287	8	~1985
7420943	14841887	8	~1985
7421143	252318863	9	~1988
7421237	44527423	8	~1986
7421363	14842727	8	~1985
7421437	44528623	8	~1986
7421681	59373449	8	~1986
7421759	14843519	8	~1985

4.783.821 digits

25-05-11