Initial data commit

Task/Circular-primes/Nim/circular-primes.nim

@@ -0,0 +1,111 @@
+import bignum
+import strformat
+
+const SmallPrimes = [
+  2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
+  101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
+  211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293,
+  307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397,
+  401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499,
+  503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599,
+  601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691,
+  701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797,
+  809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887,
+  907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]
+
+let
+  One = newInt(1)
+  Two = newInt(2)
+  Ten = newInt(10)
+
+#---------------------------------------------------------------------------------------------------
+
+proc isPrime(n: Int): bool =
+
+  if n < Two: return false
+
+  for sp in SmallPrimes:
+    # let spb = newInt(sp)
+    if n == sp: return true
+    if (n mod sp).isZero: return false
+    if n < sp * sp: return true
+
+  result = probablyPrime(n, 25) != 0
+
+#---------------------------------------------------------------------------------------------------
+
+proc cycle(n: Int): Int =
+
+  var m = n
+  var p = 1
+  while m >= Ten:
+    p *= 10
+    m = m div 10
+  result = m + Ten * (n mod p)
+
+#---------------------------------------------------------------------------------------------------
+
+proc isCircularPrime(p: Int): bool =
+
+  if not p.isPrime(): return false
+
+  var p2 = cycle(p)
+  while p2 != p:
+    if p2 < p or not p2.isPrime():
+      return false
+    p2 = cycle(p2)
+  result = true
+
+#---------------------------------------------------------------------------------------------------
+
+proc testRepunit(digits: int) =
+
+  var repunit = One
+  var count = digits - 1
+  while count > 0:
+    repunit = Ten * repunit + One
+    dec count
+  if repunit.isPrime():
+    echo fmt"R({digits}) is probably prime."
+  else:
+    echo fmt"R({digits}) is not prime."
+
+#---------------------------------------------------------------------------------------------------
+
+echo "First 19 circular primes:"
+var p = 2
+var line = ""
+var count = 0
+while count < 19:
+  if newInt(p).isCircularPrime():
+    if count > 0: line.add(", ")
+    line.add($p)
+    inc count
+  inc p
+echo line
+
+echo ""
+echo "Next 4 circular primes:"
+var repunit = One
+var digits = 1
+while repunit < p:
+  repunit = Ten * repunit + One
+  inc digits
+line = ""
+count = 0
+while count < 4:
+  if repunit.isPrime():
+    if count > 0: line.add(' ')
+    line.add(fmt"R({digits})")
+    inc count
+  repunit = Ten * repunit + One
+  inc digits
+echo line
+
+echo ""
+testRepUnit(5003)
+testRepUnit(9887)
+testRepUnit(15073)
+testRepUnit(25031)
+testRepUnit(35317)
+testRepUnit(49081)