伪素数












伪素数是指满足素数的某种性质，但并不一定是素数的数。根据所满足的性质的不同可以划分不同种类的伪素数。其中最有名的伪素数是满足费马小定理的合数，即费马伪素数。



费马伪素数


主条目：费马伪素数

费马伪素数的定义是：对自然数x{displaystyle x}x和一个与其互素的自然数a，如果x{displaystyle x}x整除 ax-1 - 1，则称x{displaystyle x}x是一个以a为底的费马伪素数或者关于a的费马伪素数。最小的费马伪素数是341（=11×31，关于2）。如果x{displaystyle x}x关于任何与其互素的数都是费马伪素数，则称x{displaystyle x}x是绝对伪素数（或卡邁克爾數），来自找到第一个绝对伪素数的数学家羅伯特·丹尼·卡邁克爾）。最小的绝对伪素数是561。



参见



  • 费马伪素数

  • 卡迈克尔数

  • 欧拉伪素数

  • 欧拉－雅可比伪素数




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