Small Mersenne Prime Factors (page 524/5775)

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
3080153	43122143	8	~1984
3080303	6160607	7	~1982
3080401	67768823	8	~1984
3080443	369653161	9	~1986
3080531	6161063	7	~1982
3080771	24646169	8	~1983
3080797	18484783	8	~1983
3080963	6161927	7	~1982
3081311	6162623	7	~1982
3081443	6162887	7	~1982
3081503	6163007	7	~1982
3081599	55468783	8	~1984
3081691	49307057	8	~1984
3081797	166417039	9	~1985
3081809	24654473	8	~1983
3081833	18490999	8	~1983
3082021	49312337	8	~1984
3082031	24656249	8	~1983
3082087	73970089	8	~1984
3082259	6164519	7	~1982
3082393	73977433	8	~1984
3082397	24659177	8	~1983
3082397	73977529	8
3082699	73984777	8	~1984
3082873	18497239	8	~1983

Exp.	Prime Factor	Digits	Year
3083021	24664169	8	~1983
3083083	30830831	8	~1983
3083189	98662049	8	~1985
3083237	18499423	8	~1983
3083279	24666233	8	~1983
3083519	518031193	9	~1986
3083701	18502207	8	~1983
3083737	92512111	8	~1985
3083891	6167783	7	~1982
3083959	55511263	8	~1984
3083963	6167927	7	~1982
3084083	6168167	7	~1982
3084217	18505303	8	~1983
3084413	18506479	8	~1983
3084427	55519687	8	~1984
3084481	863654681	9	~1987
3084733	49355729	8	~1984
3084797	18508783	8	~1983
3084797	43187159	8
3084839	6169679	7	~1982
3085067	55531207	8	~1984
3085331	6170663	7	~1982
3085349	43194887	8	~1984
3085553	43197743	8	~1984
3085603	74054473	8	~1984

Exp.	Prime Factor	Digits	Year
3085609	197478977	9	~1985
3085741	49371857	8	~1984
3085751	24686009	8	~1983
3085769	92573071	8	~1985
3085787	24686297	8	~1983
3085813	67887887	8	~1984
3085969	148126513	9	~1985
3086099	24688793	8	~1983
3086183	6172367	7	~1982
3086287	55553167	8	~1984
3086287	74070889	8
3086423	6172847	7	~1982
3086423	129629767	9
3086563	30865631	8	~1983
3086579	129636319	9	~1985
3086599	179022743	9	~1985
3086641	18519847	8	~1983
3086749	74081977	8	~1984
3086779	30867791	8	~1983
3087173	18523039	8	~1983
3087211	30872111	8	~1983
3087233	43221263	8	~1984
3087239	6174479	7	~1982
3087239	376643159	9
3087509	24700073	8	~1983

Exp.	Prime Factor	Digits	Year
3087619	30876191	8	~1983
3087653	18525919	8	~1983
3087743	6175487	7	~1982
3087901	18527407	8	~1983
3087901	49406417	8
3088073	98818337	8	~1985
3088093	49409489	8	~1984
3088121	24704969	8	~1983
3088139	24705113	8	~1983
3088147	30881471	8	~1983
3088159	55586863	8	~1984
3088201	18529207	8	~1983
3088381	18530287	8	~1983
3088517	74124409	8	~1984
3088559	24708473	8	~1983
3088573	18531439	8	~1983
3088573	49417169	8
3088607	55594927	8	~1984
3088691	6177383	7	~1982
3088711	30887111	8	~1983
3088741	18532447	8	~1983
3088753	18532519	8	~1983
3088801	18532807	8	~1983
3088801	92664031	8
3088837	18533023	8	~1983

5.471.290 digits

26-03-29