Eisenstein Primes

Apr 13 2016
Eisenstein Primes

map (\(x, y) -> (x + y * w, (x + y * w) * (x + y * w ^ 2)))
    (matchAll take 10 nats as set integer with
      | $x :: $y :: _ -> (x, y))

[(1 + w, 1), (1 + 2 * w, 3), (2 + w, 3), (1 + 3 * w, 7), (2 + 2 * w, 4),
 (3 + w, 7), (1 + 4 * w, 13), (2 + 3 * w, 7), (3 + 2 * w, 7), (4 + w, 13),
 (1 + 5 * w, 21), (2 + 4 * w, 12), (3 + 3 * w, 9), (4 + 2 * w, 12), (5 + w, 21),
 (1 + 6 * w, 31), (2 + 5 * w, 19), (3 + 4 * w, 13), (4 + 3 * w, 13),
 (5 + 2 * w, 19), (6 + w, 31), (1 + 7 * w, 43), (2 + 6 * w, 28),
 (3 + 5 * w, 19), (4 + 4 * w, 16), (5 + 3 * w, 19), (6 + 2 * w, 28),
 (7 + w, 43), (1 + 8 * w, 57), (2 + 7 * w, 39), (3 + 6 * w, 27),
 (4 + 5 * w, 21), (5 + 4 * w, 21), (6 + 3 * w, 27), (7 + 2 * w, 39),
 (8 + w, 57), (1 + 9 * w, 73), (2 + 8 * w, 52), (3 + 7 * w, 37),
 (4 + 6 * w, 28), (5 + 5 * w, 25), (6 + 4 * w, 28), (7 + 3 * w, 37),
 (8 + 2 * w, 52), (9 + w, 73), (1 + 10 * w, 91), (2 + 9 * w, 67),
 (3 + 8 * w, 49), (4 + 7 * w, 37), (5 + 6 * w, 31), (6 + 5 * w, 31),
 (7 + 4 * w, 37), (8 + 3 * w, 49), (9 + 2 * w, 67), (10 + w, 91),
 (2 + 10 * w, 84), (3 + 9 * w, 63), (4 + 8 * w, 48), (5 + 7 * w, 39),
 (6 + 6 * w, 36), (7 + 5 * w, 39), (8 + 4 * w, 48), (9 + 3 * w, 63),
 (10 + 2 * w, 84), (3 + 10 * w, 79), (4 + 9 * w, 61), (5 + 8 * w, 49),
 (6 + 7 * w, 43), (7 + 6 * w, 43), (8 + 5 * w, 49), (9 + 4 * w, 61),
 (10 + 3 * w, 79), (4 + 10 * w, 76), (5 + 9 * w, 61), (6 + 8 * w, 52),
 (7 + 7 * w, 49), (8 + 6 * w, 52), (9 + 5 * w, 61), (10 + 4 * w, 76),
 (5 + 10 * w, 75), (6 + 9 * w, 63), (7 + 8 * w, 57), (8 + 7 * w, 57),
 (9 + 6 * w, 63), (10 + 5 * w, 75), (6 + 10 * w, 76), (7 + 9 * w, 67),
 (8 + 8 * w, 64), (9 + 7 * w, 67), (10 + 6 * w, 76), (7 + 10 * w, 79),
 (8 + 9 * w, 73), (9 + 8 * w, 73), (10 + 7 * w, 79), (8 + 10 * w, 84),
 (9 + 9 * w, 81), (10 + 8 * w, 84), (9 + 10 * w, 91), (10 + 9 * w, 91),
 (10 + 10 * w, 100)]

filter
  (\(_, n) -> isPrime n)
  (map (\(x, y) -> (x + y * w, (x + y * w) * (x + y * w ^ 2)))
       (matchAll take 10 nats as set integer with
         | $x :: $y :: _ -> (x, y)))

[(1 + 2 * w, 3), (2 + w, 3), (1 + 3 * w, 7), (3 + w, 7),
 (1 + 4 * w, 13), (2 + 3 * w, 7), (3 + 2 * w, 7), (4 + w, 13), (1 + 6 * w, 31),
 (2 + 5 * w, 19), (3 + 4 * w, 13), (4 + 3 * w, 13), (5 + 2 * w, 19),
 (6 + w, 31), (1 + 7 * w, 43), (3 + 5 * w, 19), (5 + 3 * w, 19), (7 + w, 43),
 (1 + 9 * w, 73), (3 + 7 * w, 37), (7 + 3 * w, 37), (9 + w, 73),
 (2 + 9 * w, 67), (4 + 7 * w, 37), (5 + 6 * w, 31), (6 + 5 * w, 31),
 (7 + 4 * w, 37), (9 + 2 * w, 67), (3 + 10 * w, 79), (4 + 9 * w, 61),
 (6 + 7 * w, 43), (7 + 6 * w, 43), (9 + 4 * w, 61), (10 + 3 * w, 79),
 (5 + 9 * w, 61), (9 + 5 * w, 61), (7 + 9 * w, 67), (9 + 7 * w, 67),
 (7 + 10 * w, 79), (8 + 9 * w, 73), (9 + 8 * w, 73), (10 + 7 * w, 79)]
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