Grupa
Obserwarorów Zmiennego Nieba
Mersenne prime
M
n
= 2
p
– 1
Największa znana liczba pierwsza:
M
48
= 2
57885161
– 1
Liczba cyfr M48: 17,425,170
GIMPS - Great Internet Mersenne Prime Search
Czas obliczenia weryfikującego na PC: 3 tygodnie
Znane liczby pierwsze Mersenne’a
# p Mp digit s Dis cov ere dDiscoverer Method used
1 2 1 c. 430 BC Ancient Greek mathematicians 2 3 1 c. 430 BC Ancient Greek mathematicians 3 5 2 c. 300 BC Ancient Greek mathematicians 4 7 3 c. 300 BC Ancient Greek mathematicians
Znane liczby pierwsze Mersenne’a
# p Mp digit s Dis cov ere dDiscoverer Method used
5 13 4 1456 Anonymous Trial division
6 17 6 1588 Pietro Cataldi Trial division 7 19 6 1588 Pietro Cataldi Trial division 8 31 10 1772 Leonhard Euler Enhanced trial division
9 61 19 1883 I. M. Pervushin Lucas sequences
10 89 27 1911 Ralph Ernest Powers Lucas sequences 11 107 33 1914 Ralph Ernest Powers Lucas sequences 12 127 39 1876 Édouard Lucas Lucas sequences
Znane liczby pierwsze Mersenne’a
# p Mp digit s Dis cov ere dDiscoverer Method used
13 521 157 1952 Raphael M. Robinson LLT / SWAC
14 607 183 1952 Raphael M. Robinson LLT / SWAC 15 1,279 386 1952 Raphael M. Robinson LLT / SWAC 16 2,203 664 1952 Raphael M. Robinson LLT / SWAC 17 2,281 687 1952 Raphael M. Robinson LLT / SWAC 18 3,217 969 1957 Hans Riesel LLT / BESK
Znane liczby pierwsze Mersenne’a
# p Mp digit s Dis cov ere dDiscoverer Method used
19 4,253 1,281 1961 Alexander Hurwitz LLT / IBM 7090
20 4,423 1,332 1961 Alexander Hurwitz LLT / IBM 7090 21 9,689 2,917 1963 Donald B. Gillies LLT / ILLIAC II
22 9,941 2,993 1963 Donald B. Gillies LLT / ILLIAC II 23 11,213 3,376 1963 Donald B. Gillies LLT / ILLIAC II 24 19,937 6,002 1971 Bryant Tuckerman LLT / IBM 360/91
25 21,701 6,533 1978
Landon Curt Noll & Laura Nickel
LLT / CDC Cyber 174
Znane liczby pierwsze Mersenne’a
# p Mp digit
s
Yea
r Discoverer Method used
27 44,497 13,395 1979 Harry L. Nelson & David Slowinski
LLT / Cray 1
28 86,243 25,962 1982 David Slowinski LLT / Cray 1 29 110,503 33,265 1988 Walter Colquitt & Luke Welsh LLT / NEC SX-2
30 132,049 39,751 1983 David Slowinski LLT / Cray X-MP
31 216,091 65,050 1985 David Slowinski LLT / Cray X-MP/24 32 756,839 227,832 1992 David Slowinski & Paul Gage LLT /Harwell Lab’s Cray-2
33 859,433 258,716 1994 David Slowinski & Paul Gage LLT / Cray C90
Znane liczby pierwsze Mersenne’a
# p Mp digit
s
Yea
r Discoverer Method used
35 1,398,269 420,921 1996 GIMPSArmengaud / Joel LLT / 90 MHz Prime95Pentium on P C
36 2,976,221 895,932 1997 GIMPS / Gordon Spence LLT / Prime95 on 100 MHz Pentium PC
37 3,021,377 909,526 1998 GIMPS / Roland Clarkson LLT / Prime95 on 200 MHz Pentium PC
38 6,972,593 2,098,960 1999 GIMPS / Nayan Hajratwala LLT / Prime95 on 350 MHz Pentium II IBM Aptiva 39 13,466,917 4,053,946 2001 GIMPS / Michael Cameron LLT / Prime95 on 800 MHz Athlon T-Bird
40 20,996,011 6,320,430 2003 GIMPS / Michael Shafer
LLT / Prime95 on 2 GHz Dell
Znane liczby pierwsze Mersenne’a
# p Mp digit
s
Yea
r Discoverer Method used
41 24,036,583 7,235,733 2004 GIMPS / Josh Findley LLT / Prime95 on 2.4 GHz Pentium 4 PC
42 25,964,951 7,816,230 2005 GIMPS / Martin Nowak LLT / Prime95 on 2.4 GHz Pentium 4 PC
43 30,402,457 9,152,052 2005 GIMPS / Cooper & Curtis Steven Boone
LLT / Prime95 on 2 GHz Pentium 4 PC
44 32,582,657 9,808,358 2006 GIMPS / Curtis Cooper & Steven Boone
LLT / Prime95 on 3 GHz Pentium 4 PC
45 37,156,667 11,185,272 2008 GIMPS / Hans-Michael Elvenich
LLT / Prime95 on 2.83 GHz Core 2 Duo PC
Znane liczby pierwsze Mersenne’a
# p Mp digit
s
Yea
r Discoverer Method used
46 42,643,801 12,837,064 2009 GIMPS / Odd M. Strindmo LLT / Prime95 on 3 GHz Core 2 PC
47 43,112,609 12,978,189 2008 GIMPS / Edson Smith LLT / Prime95 on Dell Optiplex 745 48 57,885,161 17,425,170 2013 GIMPS / Curtis Cooper
LLT / Prime95 on 3 GHz Intel Core2 Duo E8400