Small Mersenne Prime Factors (page 891/5205)

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
7800973	46805839	8	~1986
7801337	46808023	8	~1986
7801373	46808239	8	~1986
7801823	15603647	8	~1985
7801919	15603839	8	~1985
7802117	109229639	9	~1987
7802213	109230983	9	~1987
7802339	15604679	8	~1985
7802413	46814479	8	~1986
7802551	124840817	9	~1987
7802791	140450239	9	~1987
7802849	109239887	9	~1987
7803193	46819159	8	~1986
7803613	46821679	8	~1986
7803749	62429993	8	~1986
7803839	15607679	8	~1985
7803973	46823839	8	~1986
7804271	15608543	8	~1985
7804501	46827007	8	~1986
7805081	62440649	8	~1986
7805107	702459631	9	~1989
7805177	1795190711	10	~1990
7805201	46831207	8	~1986
7805297	46831783	8	~1986
7805939	62447513	8	~1986

Exp.	Prime Factor	Digits	Year
7805957	46835743	8	~1986
7805957	62447657	8
7806013	46836079	8	~1986
7806311	62450489	8	~1986
7806433	46838599	8	~1986
7806479	15612959	8	~1985
7806797	62454377	8	~1986
7806863	15613727	8	~1985
7806983	15613967	8	~1985
7807361	62458889	8	~1986
7807531	78075311	8	~1987
7807601	46845607	8	~1986
7807637	62461097	8	~1986
7808441	46850647	8	~1986
7808483	15616967	8	~1985
7808503	78085031	8	~1987
7808519	15617039	8	~1985
7808579	577834847	9	~1989
7808617	46851703	8	~1986
7808617	124937873	9
7808657	62469257	8	~1986
7808699	62469593	8	~1986
7808699	327965359	9
7808711	15617423	8	~1985
7808839	78088391	8	~1987

Exp.	Prime Factor	Digits	Year
7808897	46853383	8	~1986
7809083	15618167	8	~1985
7809491	15618983	8	~1985
7809533	46857199	8	~1986
7809601	46857607	8	~1986
7809757	46858543	8	~1986
7809793	46858759	8	~1986
7809821	62478569	8	~1986
7809911	15619823	8	~1985
7810057	46860343	8	~1986
7810333	187447993	9	~1987
7810421	46862527	8	~1986
7810619	15621239	8	~1985
7810721	46864327	8	~1986
7810739	15621479	8	~1985
7810931	15621863	8	~1985
7810987	124975793	9	~1987
7811057	46866343	8	~1986
7811173	46867039	8	~1986
7811203	124979249	9	~1987
7811543	15623087	8	~1985
7811561	62492489	8	~1986
7811663	515569759	9	~1989
7811879	15623759	8	~1985
7812071	15624143	8	~1985

Exp.	Prime Factor	Digits	Year
7812121	171866663	9	~1987
7812179	62497433	8	~1986
7812599	15625199	8	~1985
7813037	62504297	8	~1986
7813109	62504873	8	~1986
7813241	46879447	8	~1986
7813343	15626687	8	~1985
7813451	15626903	8	~1985
7813801	46882807	8	~1986
7813853	46883119	8	~1986
7813979	15627959	8	~1985
7814413	46886479	8	~1986
7814783	15629567	8	~1985
7814819	15629639	8	~1985
7814837	46889023	8	~1986
7814843	15629687	8	~1985
7815281	62522249	8	~1986
7815397	46892383	8	~1986
7815629	62525033	8	~1986
7815737	46894423	8	~1986
7815793	46894759	8	~1986
7816271	15632543	8	~1985
7816463	15632927	8	~1985
7816513	46899079	8	~1986
7816513	312660521	9

4.903.097 digits

25-07-08