質數問題(p,2002+p,2002-p)－香港介紹ppt

標題:

質數問題(p,2002+p,2002-p)

發問:

如果p係質數 2002+p係質數,2002-p又係質數 p最小值? 點計? 更新: P係質數!!!! 有冇公式計到呢條數? 更新 2: 好似冇人問我講咩我係話 p 同 2002+p同2002-p 3個數全部都係質數!!!!!!! 唔係3個之中有1個係質數!!!!!!!

最佳解答:

有的三個數 2002+p p 2002-p 若p係3n(n係一個整數) 係3n+1(n係一個整數) 係3n+2(n係一個整數) 2002+3n 3n 2002-3n 2002+3n+1 3n+1 2002-(3n+1) 2002+3n+2 3n+2 2002-(3n+2) 以上3個情況都必有一個係3ge倍數因此3ge倍數中得3係質數因此2002+p p 2002-p中是但一個係3 2002+p不可能是3 如果p=3,2005不是質數因此只有2002-3 姐係1999

其他解答:

By trial and error method: p = 1, 2002 - 1 = 2001 = 3 x 667 p = 2, 4, 6, 8 and 0 are all even numbers. p = 3, 2002 + 3 = 2005 = 5 x 401. p = 5, 2002 + 5 = 2007 = 3 x 669. p = 7, 2002 - 7 = 1995 = 5 x 399. p = 9, 2002 + 9 = 2011, 2002 - 9 = 1993, both are prime numbers, so p = 9.