Gaussian primes: Difference between revisions

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                                                                                                      </pre>
+=={{header|Nim}}==
+{{libheader|gnuplotlib.nim}}
+<syntaxhighlight lang="Nim">import std/[algorithm, math, strformat]
+import gnuplot
+type IntComplex = tuple[re, im: int]
+func isPrime(n: Natural): bool =
+  if n < 2: return false
+  if (n and 1) == 0: return n == 2
+  var d = 3
+  while d * d <= n:
+    if n mod d == 0:
+      return false
+    inc d, 2
+  result = true
+func norm(c: IntComplex): Natural =
+  c.re * c.re + c.im * c.im
+func `$`(c: IntComplex): string =
+  if c.im == 0: return $c.re
+  if c.re == 0: return $c.im & 'i'
+  let op = if c.im > 0: '+' else: '-'
+  result = &"{c.re}{op}{abs(c.im)}i"
+func isGaussianPrime(c: IntComplex): bool =
+  if c.re == 0:
+    let x = abs(c.im)
+    return x.isPrime and (x and 3) == 3
+  if c.im == 0:
+    let x = abs(c.re)
+    return x.isPrime and (x and 3) == 3
+  result = c.norm.isPrime
+func gaussianPrimes(maxNorm: Positive): seq[IntComplex] =
+  var gpList: seq[IntComplex]
+  let m = sqrt(maxNorm.toFloat).int
+  for x in -m..m:
+    for y in -m..m:
+      let c = (x, y)
+      if c.norm < maxNorm and c.isGaussianPrime:
+        gpList.add c
+  result = gpList.sortedByIt(it.norm)
+echo "Gaussian primes with a norm less than 100 sorted by norm:"
+for i, gp in gaussianPrimes(100):
+  stdout.write &"{gp:>5}"
+  stdout.write if i mod 10 == 9: '\n' else: ' '
+var x, y: seq[int]
+for gp in gaussianPrimes(150^2):
+  x.add gp.re
+  y.add gp.im
+withGnuPlot:
+  cmd "set size ratio -1"
+  plot(x, y, "Gaussian primes", "with dots lw 2")
+</syntaxhighlight>
+{{out}}
+<pre>Gaussian primes with a norm less than 100 sorted by norm:
+-1-1i -1+1i  1-1i  1+1i -2-1i -2+1i -1-2i -1+2i  1-2i  1+2i
+-1i  2+1i    -3   -3i    3i     3 -3-2i -3+2i -2-3i -2+3i
+-3i  2+3i  3-2i  3+2i -4-1i -4+1i -1-4i -1+4i  1-4i  1+4i
+-1i  4+1i -5-2i -5+2i -2-5i -2+5i  2-5i  2+5i  5-2i  5+2i
+-6-1i -6+1i -1-6i -1+6i  1-6i  1+6i  6-1i  6+1i -5-4i -5+4i
+-4-5i -4+5i  4-5i  4+5i  5-4i  5+4i    -7   -7i    7i     7
+-7-2i -7+2i -2-7i -2+7i  2-7i  2+7i  7-2i  7+2i -6-5i -6+5i
+-5-6i -5+6i  5-6i  5+6i  6-5i  6+5i -8-3i -8+3i -3-8i -3+8i
+-8i  3+8i  8-3i  8+3i -8-5i -8+5i -5-8i -5+8i  5-8i  5+8i
+-5i  8+5i -9-4i -9+4i -4-9i -4+9i  4-9i  4+9i  9-4i  9+4i
+</pre>
 =={{header|Perl}}==