Gaussian Primes

Gaussian Primes

(map 2#[(+ %1 (* i %2)) (* (+ %1 (* i %2)) (+ %1 (* -1 i %2)))] (match-all (take 10 nats) (set integer) [<cons $x <cons $y _>> [x y]])) {[(+ 1 i) 2] [(+ 1 (* 2 i)) 5] [(+ 2 i) 5] [(+ 1 (* 3 i)) 10] [(+ 2 (* 2 i)) 8] [(+ 3 i) 10] [(+ 1 (* 4 i)) 17] [(+ 2 (* 3 i)) 13] [(+ 3 (* 2 i)) 13] [(+ 4 i) 17] [(+ 1 (* 5 i)) 26] [(+ 2 (* 4 i)) 20] [(+ 3 (* 3 i)) 18] [(+ 4 (* 2 i)) 20] [(+ 5 i) 26] [(+ 1 (* 6 i)) 37] [(+ 2 (* 5 i)) 29] [(+ 3 (* 4 i)) 25] [(+ 4 (* 3 i)) 25] [(+ 5 (* 2 i)) 29] [(+ 6 i) 37] [(+ 1 (* 7 i)) 50] [(+ 2 (* 6 i)) 40] [(+ 3 (* 5 i)) 34] [(+ 4 (* 4 i)) 32] [(+ 5 (* 3 i)) 34] [(+ 6 (* 2 i)) 40] [(+ 7 i) 50] [(+ 1 (* 8 i)) 65] [(+ 2 (* 7 i)) 53] [(+ 3 (* 6 i)) 45] [(+ 4 (* 5 i)) 41] [(+ 5 (* 4 i)) 41] [(+ 6 (* 3 i)) 45] [(+ 7 (* 2 i)) 53] [(+ 8 i) 65] [(+ 1 (* 9 i)) 82] [(+ 2 (* 8 i)) 68] [(+ 3 (* 7 i)) 58] [(+ 4 (* 6 i)) 52] [(+ 5 (* 5 i)) 50] [(+ 6 (* 4 i)) 52] [(+ 7 (* 3 i)) 58] [(+ 8 (* 2 i)) 68] [(+ 9 i) 82] [(+ 1 (* 10 i)) 101] [(+ 2 (* 9 i)) 85] [(+ 3 (* 8 i)) 73] [(+ 4 (* 7 i)) 65] [(+ 5 (* 6 i)) 61] [(+ 6 (* 5 i)) 61] [(+ 7 (* 4 i)) 65] [(+ 8 (* 3 i)) 73] [(+ 9 (* 2 i)) 85] [(+ 10 i) 101] [(+ 2 (* 10 i)) 104] [(+ 3 (* 9 i)) 90] [(+ 4 (* 8 i)) 80] [(+ 5 (* 7 i)) 74] [(+ 6 (* 6 i)) 72] [(+ 7 (* 5 i)) 74] [(+ 8 (* 4 i)) 80] [(+ 9 (* 3 i)) 90] [(+ 10 (* 2 i)) 104] [(+ 3 (* 10 i)) 109] [(+ 4 (* 9 i)) 97] [(+ 5 (* 8 i)) 89] [(+ 6 (* 7 i)) 85] [(+ 7 (* 6 i)) 85] [(+ 8 (* 5 i)) 89] [(+ 9 (* 4 i)) 97] [(+ 10 (* 3 i)) 109] [(+ 4 (* 10 i)) 116] [(+ 5 (* 9 i)) 106] [(+ 6 (* 8 i)) 100] [(+ 7 (* 7 i)) 98] [(+ 8 (* 6 i)) 100] [(+ 9 (* 5 i)) 106] [(+ 10 (* 4 i)) 116] [(+ 5 (* 10 i)) 125] [(+ 6 (* 9 i)) 117] [(+ 7 (* 8 i)) 113] [(+ 8 (* 7 i)) 113] [(+ 9 (* 6 i)) 117] [(+ 10 (* 5 i)) 125] [(+ 6 (* 10 i)) 136] [(+ 7 (* 9 i)) 130] [(+ 8 (* 8 i)) 128] [(+ 9 (* 7 i)) 130] [(+ 10 (* 6 i)) 136] [(+ 7 (* 10 i)) 149] [(+ 8 (* 9 i)) 145] [(+ 9 (* 8 i)) 145] [(+ 10 (* 7 i)) 149] [(+ 8 (* 10 i)) 164] [(+ 9 (* 9 i)) 162] [(+ 10 (* 8 i)) 164] [(+ 9 (* 10 i)) 181] [(+ 10 (* 9 i)) 181] [(+ 10 (* 10 i)) 200] } (filter 2#(prime? %2) (map 2#[(+ %1 (* i %2)) (* (+ %1 (* i %2)) (+ %1 (* -1 i %2)))] (match-all (take 10 nats) (set integer) [<cons $x <cons $y _>> [x y]]))) {[(+ 1 i) 2] [(+ 1 (* 2 i)) 5] [(+ 2 i) 5] [(+ 1 (* 4 i)) 17] [(+ 2 (* 3 i)) 13] [(+ 3 (* 2 i)) 13] [(+ 4 i) 17] [(+ 1 (* 6 i)) 37] [(+ 2 (* 5 i)) 29] [(+ 5 (* 2 i)) 29] [(+ 6 i) 37] [(+ 2 (* 7 i)) 53] [(+ 4 (* 5 i)) 41] [(+ 5 (* 4 i)) 41] [(+ 7 (* 2 i)) 53] [(+ 1 (* 10 i)) 101] [(+ 3 (* 8 i)) 73] [(+ 5 (* 6 i)) 61] [(+ 6 (* 5 i)) 61] [(+ 8 (* 3 i)) 73] [(+ 10 i) 101] [(+ 3 (* 10 i)) 109] [(+ 4 (* 9 i)) 97] [(+ 5 (* 8 i)) 89] [(+ 8 (* 5 i)) 89] [(+ 9 (* 4 i)) 97] [(+ 10 (* 3 i)) 109] [(+ 7 (* 8 i)) 113] [(+ 8 (* 7 i)) 113] [(+ 7 (* 10 i)) 149] [(+ 10 (* 7 i)) 149] [(+ 9 (* 10 i)) 181] [(+ 10 (* 9 i)) 181] }

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