Data commit

Task/Pierpont-primes/Python/pierpont-primes.py

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+import random
+
+# Copied from https://rosettacode.org/wiki/Miller-Rabin_primality_test#Python
+def is_Prime(n):
+    """
+    Miller-Rabin primality test.
+
+    A return value of False means n is certainly not prime. A return value of
+    True means n is very likely a prime.
+    """
+    if n!=int(n):
+        return False
+    n=int(n)
+    #Miller-Rabin test for prime
+    if n==0 or n==1 or n==4 or n==6 or n==8 or n==9:
+        return False
+
+    if n==2 or n==3 or n==5 or n==7:
+        return True
+    s = 0
+    d = n-1
+    while d%2==0:
+        d>>=1
+        s+=1
+    assert(2**s * d == n-1)
+
+    def trial_composite(a):
+        if pow(a, d, n) == 1:
+            return False
+        for i in range(s):
+            if pow(a, 2**i * d, n) == n-1:
+                return False
+        return True
+
+    for i in range(8):#number of trials
+        a = random.randrange(2, n)
+        if trial_composite(a):
+            return False
+
+    return True
+
+def pierpont(ulim, vlim, first):
+    p = 0
+    p2 = 1
+    p3 = 1
+    pp = []
+    for v in xrange(vlim):
+        for u in xrange(ulim):
+            p = p2 * p3
+            if first:
+                p = p + 1
+            else:
+                p = p - 1
+            if is_Prime(p):
+                pp.append(p)
+            p2 = p2 * 2
+        p3 = p3 * 3
+        p2 = 1
+    pp.sort()
+    return pp
+
+def main():
+    print "First 50 Pierpont primes of the first kind:"
+    pp = pierpont(120, 80, True)
+    for i in xrange(50):
+        print "%8d " % pp[i],
+        if (i - 9) % 10 == 0:
+            print
+    print "First 50 Pierpont primes of the second kind:"
+    pp2 = pierpont(120, 80, False)
+    for i in xrange(50):
+        print "%8d " % pp2[i],
+        if (i - 9) % 10 == 0:
+            print
+    print "250th Pierpont prime of the first kind:", pp[249]
+    print "250th Pierpont prime of the second kind:", pp2[249]
+
+main()