What 5 Numbers; Including 0, 2 Even And 2 Odd For A Formula That Yields Prime Numbers?

If you have a formula that supposedly yields prime numbers, the idea here is to check to see if it really does. You are to pick 5 numbers to try in the formula. An easy choice meeting the required conditions might be
  0    (you must include 0)
  1    (odd)
  2    (even)
  3    (odd)
  4    (even)
This list (above) has 2 odd, 2 even, and 0. It might be more interesting to try some numbers farther apart. For example, you might want to try
  0    (you must include 0)
  22    (even)
  51    (odd)
  64    (even)
  75    (odd)

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If the formula is
  F(x) = x² + x + 41
then
  F(22) = 22² + 22 + 41 = 484 + 22 + 41 = 506 + 41 = 547
This table shows 547 to be prime.
  F(51) = 51² + 51 + 41 = 2693 (prime)
  F(64) = 64² + 64 + 41 = 4201 (prime)
  F(75) = 75² + 75 + 41 = 5741 (prime)
As suggested in another answer, you could also check x=41.
  F(41) = 41² + 41 + 41 = 1763 = 41*43 (not prime)
I just made up the above numbers. I am somewhat surprised to see they all (except 41) give primes.