Small Mersenne Prime Factors (page 778/5205)

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
6181943	12363887	8	~1984
6182243	12364487	8	~1984
6182459	111284263	9	~1986
6182537	49460297	8	~1985
6182783	12365567	8	~1984
6183011	12366023	8	~1984
6183011	49464089	8
6183217	37099303	8	~1985
6183361	98933777	8	~1986
6183371	556503391	9	~1988
6183431	12366863	8	~1984
6183581	49468649	8	~1985
6183839	12367679	8	~1984
6183893	37103359	8	~1985
6184349	49474793	8	~1985
6184463	12368927	8	~1984
6184601	49476809	8	~1985
6184637	37107823	8	~1985
6184679	49477433	8	~1985
6184681	37108087	8	~1985
6184933	37109599	8	~1985
6185099	49480793	8	~1985
6185189	49481513	8	~1985
6185261	49482089	8	~1985
6185303	12370607	8	~1984

Exp.	Prime Factor	Digits	Year
6185537	86597519	8	~1986
6185759	12371519	8	~1984
6185831	12371663	8	~1984
6186083	12372167	8	~1984
6186263	12372527	8	~1984
6186359	49490873	8	~1985
6186407	160846583	9	~1987
6186503	12373007	8	~1984
6186619	148478857	9	~1987
6187367	49498937	8	~1985
6187393	37124359	8	~1985
6187477	37124863	8	~1985
6187637	86626919	8	~1986
6187661	37125967	8	~1985
6187771	259886383	9	~1987
6187799	12375599	8	~1984
6187859	12375719	8	~1984
6187871	12375743	8	~1984
6188009	86632127	8	~1986
6188059	61880591	8	~1986
6188297	37129783	8	~1985
6188401	99014417	8	~1986
6188531	12377063	8	~1984
6188789	1571952407	10	~1989
6189077	37134463	8	~1985

Exp.	Prime Factor	Digits	Year
6189083	12378167	8	~1984
6189251	12378503	8	~1984
6189299	12378599	8	~1984
6189539	12379079	8	~1984
6189593	37137559	8	~1985
6189671	12379343	8	~1984
6189727	61897271	8	~1986
6189983	12379967	8	~1984
6190259	12380519	8	~1984
6190319	12380639	8	~1984
6190423	61904231	8	~1986
6190469	185714071	9	~1987
6190799	12381599	8	~1984
6190991	12381983	8	~1984
6191279	49530233	8	~1985
6191411	12382823	8	~1984
6191461	37148767	8	~1985
6191491	99063857	8	~1986
6191597	37149583	8	~1985
6191743	61917431	8	~1986
6192161	37152967	8	~1985
6192337	37154023	8	~1985
6192523	61925231	8	~1986
6192707	148624969	9	~1987
6192749	49541993	8	~1985

Exp.	Prime Factor	Digits	Year
6192779	12385559	8	~1984
6192799	111470383	9	~1986
6192821	49542569	8	~1985
6192869	49542953	8	~1985
6192871	99085937	8	~1986
6193007	111474127	9	~1986
6193093	37158559	8	~1985
6193381	37160287	8	~1985
6193897	297307057	9	~1987
6194099	12388199	8	~1984
6194119	396423617	9	~1988
6194147	161047823	9	~1987
6194387	408829543	9	~1988
6194483	12388967	8	~1984
6194819	12389639	8	~1984
6194879	12389759	8	~1984
6194879	49559033	8
6194911	545152169	9	~1988
6194939	12389879	8	~1984
6195419	12390839	8	~1984
6195481	3605769943	10	~1990
6195601	37173607	8	~1985
6195823	61958231	8	~1986
6195863	12391727	8	~1984
6196027	61960271	8	~1986

4.903.097 digits

25-07-08