Small Mersenne Prime Factors (page 358/5490)

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
1746109	52383271	8	~1983
1746203	3492407	7	~1980
1746209	13969673	8	~1981
1746209	24446927	8
1746209	41909017	8
1746259	41910217	8	~1982
1746301	10477807	8	~1981
1746539	41916937	8	~1982
1746557	24451799	8	~1982
1746587	181645049	9	~1984
1746683	3493367	7	~1980
1746761	275988239	9	~1984
1746847	17468471	8	~1981
1746883	41925193	8	~1982
1746907	27950513	8	~1982
1746911	13975289	8	~1981
1747079	3494159	7	~1980
1747153	10482919	8	~1981
1747301	10483807	8	~1981
1747331	13978649	8	~1981
1747519	17475191	8	~1981
1747573	125825257	9	~1984
1747591	31456639	8	~1982
1747643	45438719	8	~1982
1747699	755005969	9	~1985

Exp.	Prime Factor	Digits	Year
1747951	143331983	9	~1984
1747979	3495959	7	~1980
1748003	3496007	7	~1980
1748027	87401351	8	~1983
1748177	24474479	8	~1982
1748489	52454671	8	~1983
1748639	3497279	7	~1980
1748653	52459591	8	~1983
1748723	3497447	7	~1980
1748849	13990793	8	~1981
1748891	13991129	8	~1981
1748911	17489111	8	~1981
1749031	17490311	8	~1981
1749089	24487247	8	~1982
1749107	13992857	8	~1981
1749179	3498359	7	~1980
1749233	10495399	8	~1981
1749239	3498479	7	~1980
1749239	31486303	8
1749263	87463151	8	~1983
1749383	3498767	7	~1980
1749431	3498863	7	~1980
1749673	38492807	8	~1982
1749697	10498183	8	~1981
1749701	10498207	8	~1981

Exp.	Prime Factor	Digits	Year
1749731	13997849	8	~1981
1749749	13997993	8	~1981
1749859	73494079	8	~1983
1749899	3499799	7	~1980
1749911	3499823	7	~1980
1749911	13999289	8
1749961	38499143	8	~1982
1750103	3500207	7	~1980
1750159	17501591	8	~1981
1750459	42011017	8	~1982
1750499	3500999	7	~1980
1750501	10503007	8	~1981
1750513	52515391	8	~1983
1750687	42016489	8	~1982
1750751	3501503	7	~1980
1750811	3501623	7	~1980
1750913	24512783	8	~1982
1750927	70037081	8	~1983
1750937	42022489	8	~1982
1751041	10506247	8	~1981
1751273	52538191	8	~1983
1751311	70052441	8	~1983
1751327	14010617	8	~1981
1751567	31528207	8	~1982
1751623	73568167	8	~1983

Exp.	Prime Factor	Digits	Year
1751699	3503399	7	~1980
1751753	94594663	8	~1983
1751891	3503783	7	~1980
1752029	192723191	9	~1984
1752119	3504239	7	~1980
1752319	70092761	8	~1983
1752323	3504647	7	~1980
1752341	10514047	8	~1981
1752539	3505079	7	~1980
1752563	3505127	7	~1980
1752659	3505319	7	~1980
1752679	17526791	8	~1981
1752851	31551319	8	~1982
1752923	3505847	7	~1980
1752943	70117721	8	~1983
1752977	10517863	8	~1981
1752979	17529791	8	~1981
1753007	14024057	8	~1981
1753039	17530391	8	~1981
1753109	56099489	8	~1983
1753343	3506687	7	~1980
1753441	10520647	8	~1981
1753777	28060433	8	~1982
1753777	42090649	8
1753777	4040702209	10

5.187.277 digits

25-11-17