Small Mersenne Prime Factors (page 343/5745)

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
1610153	38643673	8	~1982
1610183	67627687	8	~1983
1610309	61191743	8	~1983
1610353	35427767	8	~1982
1610527	64421081	8	~1983
1610591	28990639	8	~1982
1610627	38655049	8	~1982
1610753	293157047	9	~1984
1610783	3221567	7	~1979
1610927	12887417	8	~1981
1610963	67660447	8	~1983
1610963	193315561	9
1610969	38663257	8	~1982
1611031	67663303	8	~1983
1611059	67664479	8	~1983
1611157	74113223	8	~1983
1611289	64451561	8	~1983
1611319	132128159	9	~1983
1611331	64453241	8	~1983
1611419	12891353	8	~1981
1611517	9669103	7	~1981
1611539	3223079	7	~1979
1611563	3223127	7	~1979
1611601	9669607	7	~1981
1611607	38678569	8	~1982

Exp.	Prime Factor	Digits	Year
1611853	25789649	8	~1982
1611899	3223799	7	~1979
1611917	22566839	8	~1982
1611971	3223943	7	~1979
1612033	9672199	7	~1981
1612181	12897449	8	~1981
1612183	64487321	8	~1983
1612223	3224447	7	~1979
1612319	1973478457	10	~1986
1612333	9673999	7	~1981
1612427	106420183	9	~1983
1612693	9676159	7	~1981
1612703	3225407	7	~1979
1612763	106442359	9	~1983
1612823	3225647	7	~1979
1612997	12903977	8	~1981
1613033	22582463	8	~1982
1613041	9678247	7	~1981
1613057	9678343	7	~1981
1613057	12904457	8
1613323	16133231	8	~1981
1613483	3226967	7	~1979
1613669	12909353	8	~1981
1613981	100066823	9	~1983
1614023	3228047	7	~1979

Exp.	Prime Factor	Digits	Year
1614307	29057527	8	~1982
1614377	48431311	8	~1982
1614443	3228887	7	~1979
1614461	12915689	8	~1981
1614479	3228959	7	~1979
1614479	38747497	8
1614491	3228983	7	~1979
1614593	38750233	8	~1982
1614593	51666977	8
1614631	25834097	8	~1982
1614637	9687823	7	~1981
1614659	3229319	7	~1979
1614659	12917273	8
1614911	3229823	7	~1979
1615001	12920009	8	~1981
1615073	100134527	9	~1983
1615231	29074159	8	~1982
1615253	22613543	8	~1982
1615307	38767369	8	~1982
1615483	67850287	8	~1983
1615499	3230999	7	~1979
1615501	9693007	7	~1981
1615511	3231023	7	~1979
1615511	12924089	8
1615643	3231287	7	~1979

Exp.	Prime Factor	Digits	Year
1615777	48473311	8	~1982
1615837	38780089	8	~1982
1615837	74328503	8
1615871	90488777	8	~1983
1615949	61406063	8	~1983
1616099	3232199	7	~1979
1616497	48494911	8	~1982
1616621	9699727	7	~1981
1616627	77598097	8	~1983
1616651	3233303	7	~1979
1616861	116413993	9	~1983
1616897	9701383	7	~1981
1617433	9704599	7	~1981
1617443	3234887	7	~1979
1617503	3235007	7	~1979
1617569	126170383	9	~1983
1617647	12941177	8	~1981
1617743	3235487	7	~1979
1617779	29120023	8	~1982
1617883	16178831	8	~1981
1617893	9707359	7	~1981
1617929	12943433	8	~1981
1618087	25889393	8	~1982
1618087	55014959	8
1618223	3236447	7	~1979

5.441.361 digits

26-03-15