Lab 6

[BertLisser]

--ex5 (45 min)
carmichael :: [Integer]
carmichael = [ (6*k+1)*(12*k+1)*(18*k+1) |
          k <- [2..],
          prime (6*k+1),
          prime (12*k+1),
          prime (18*k+1)]

-- Al tested Carmichael numbers test true with Fermats primality test.
-- Carmichael numbers have the property we test with Fermats little theorem,
-- namely that if p is a prime number, then for any int b, the number b^p - b
-- is an int multiple of p.

Unclear report.
Why not taking k=1.
The question was what is the minimal Carmichael number which fools the test.

Exercise 6.
The following is a wrong conclusion.
The definition of ex6 must be parametrized by k. k=1,2,3.

-- All tested Carmichael numbers test false with MR primality test.
-- MR weeds out (most) Carmichael numbers because it also tests for a
-- non-trivial root of unity.
-- https://cs.stackexchange.com/questions/21462/why-miller-rabin-instead-of-fermat-primality-test

ex6 :: IO()
ex6 = ex6' carmichael

ex6' :: [Integer] -> IO()
ex6' (x:xs) = do
  print(x)
  res <- primeMR 10 x
  print(res)
  ex6' xs