code: def jacobi_witness(x, n):
      '''Returns False if n is an Euler pseudo-prime with base x, and
      True otherwise.
      '''
      j = jacobi(x, n) % n
      f = pow(x, n >> 1, n)
      return j != f jacobi_witness(x, n):
      '''Returns False if n is an Euler pseudo-prime with base x, and
      True otherwise.
      '''
      j = jacobi(x, n) % n
      f = pow(x, n >> 1, n)
      return j != f
docs: Returns False if n is an Euler pseudo-prime with base x, and
      True otherwise.