Euler problem 27.2

p_27 = -(2 * a - 1) * (a ^ 2 - a + 41)
  where
    n = 1000
    m = head $ filter (\x -> x ^ 2 - x + 41 > n) [1 ..]
    a = m - 1

This is the “official” Haskell solution to Euler Problem 27.

This solution is incomprehensible. The following hints are as far as I can get.

Prerequisite Considerations:

b must be a prime number, since x^2 + a*x + b must be a prime number when n=0.
a = m - 1 is a choice of the prime number b (in x^2 + a*x + b) just(?) smaller than 1000.

When a == 32,

(\x -> x^2 - x + 41) 31 == 971

Why not the prime number 997?

— Me@2015.06.14 08:53 AM

It is because 997 is not a prime number generated by the formula x^2 - x + 41.

— Me@2015-06-30 11:07:53 AM

The code

l = map (\x -> x^2 - x + 41) [0..40]

is for generating 41 primes with the greatest Euler’s lucky number 41.

— Me@2015.06.14 08:34 AM

λ> :set +s
λ> p_27
[-59231,-61,971]
(0.00 secs, 113,624 bytes)
λ>

— Me@2025-03-24 01:20:37 PM