n n Gauss 1777 1855 Legendre 1752 1833
- Slides: 74
質數數量估計 n n 高斯Gauss (1777 – 1855) Legendre (1752 – 1833)
質數定理 n n Jacques Salomon Hadamard (1865 – 1963) Charles Jean de la Vallée-Poussin (1866 – 1962) 這兩人在同一年, 都用複變函數方法 證明了質數定理。
質數定理 n n Paul Erdős (1913 – 1996) Atle Selberg (1917 – 2007) 「一定有初等證明!」
Fibonacci Number Fibonacci, Leonardo of Pisa (1170 – 1250)
費波那契數 1 1 2 1 3 2 4 3 5 5 6 8 7 8 9 10 13 21 34 55 17 11 12 13 14 15 16 89 144 233 377 610 987 18 19 20 1597 2584 4181 6765
費波那契數 1 1 2 1 3 2 4 3 5 5 6 8 7 8 9 10 13 21 34 55 17 11 12 13 14 15 16 89 144 233 377 610 987 18 19 20 1597 2584 4181 6765
費波那契數 1 1 2 1 3 2 4 3 5 5 6 8 7 8 9 10 13 21 34 55 17 11 12 13 14 15 16 89 144 233 377 610 987 18 19 20 1597 2584 4181 6765
費波那契數 1 1 2 1 3 2 4 3 5 5 6 8 7 8 9 10 13 21 34 55 17 11 12 13 14 15 16 89 144 233 377 610 987 18 19 20 1597 2584 4181 6765
費波那契數 1 1 2 1 3 2 4 3 5 5 6 8 7 8 9 10 13 21 34 55 17 11 12 13 14 15 16 89 144 233 377 610 987 18 19 20 1597 2584 4181 6765
Fermat Number Pierre de Fermat (160? – 1665)
Fermat Number 它們都是質數 ?
Mersenne Number Marin Mersenne (1588 – 1648)
梅森數 1 1 n 2 3 3 4 5 6 7 7 15 31 63 127 梅森質數! 8 255 9 10 511 1023
大質數發現史 n n n G reat Internet M ersenne P rime Search GIMPS 1996年開始 目前世界上已知最大的13個梅森質數
Discovery date Prime Digits Name 13 November 1996 M 1398269 420, 921 M 35 24 August 1997 M 2976221 895, 932 M 36 27 January 1998 M 3021377 909, 526 M 37 1 June 1999 M 6972593 2, 098, 960 M 38 14 November 2001 M 13466917 4, 053, 946 M 39 17 November 2003 M 20996011 6, 320, 430 M 40 ? 15 May 2004 M 24036583 7, 235, 733 M 41 ? 18 February 2005 M 25964951 7, 816, 230 M 42 ? 15 December 2005 M 30402457 9, 152, 052 M 43 ? 4 September 2006 M 32582657 9, 808, 358 M 44 ? 23 August 2008 M 43112609 12, 978, 189 M 47 ? 6 September 2008 M 37156667 11, 185, 272 M 45 ? 12 April 2009 M 42643801 12, 837, 064 M 46 ?
梅森質數的檢驗 n n Édouard Lucas (1842 – 1891) Derrick Henry Lehmer (1905 – 1991)
Lucas-Lehmer 質數檢驗法 n n 定義一個遞迴數列: 前幾項是 4, 194, 37634, 1416317954, 2005956546822746114, 4023861667741036022825635656102100994, 16191462721115671781777559070120513664958590125499 … 158514329308740975788034 當 是奇質數的時候, 是質數若且唯若
THE END
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