Initial Commit

Python/Prime cracker/Prime cracker.py

@@ -0,0 +1,39 @@
+def loop(n,depth):
+    """generates numbers containing "depth" primes, up to n"""
+    if depth==0:            #generates the powers of two
+        num1=1    
+        while num1<n/2:
+            num1*=pr[0]
+            yield num1
+    else:
+        for i in loop(n,depth-1):           #generates all numbers containing the first n prime numbers
+            num_depth=i                     #number containing all previous primes
+            while num_depth<n/pr[depth]:
+                num_depth*=primes[depth]            #successively multiplies the nth prime
+                yield num_depth
+
+def admissiblenums(n=1e9):
+    """generates a set of all admissible numbers not exceeding 1e9"""
+    admissibleset=set()
+    for i in range(len(pr)):
+        nth_admissible_prime=set(loop(n,i))
+        admissibleset|=nth_admissible_prime     #union of admissibles up to nth prime   
+    return admissibleset
+
+
+def pseudofortunate(n):
+    """returns the pseudofortunate number of n
+    (the difference between n, and the first prime larger than or equal to n)"""
+    prime_candidate=n+3#defined as prime larger than n+1, so starting the search for a prime at n+3, since admissible numbers are always even
+    while True:
+        if is_prime(m):
+            return prime_candidate-n        #returns the difference(pseudo-fortunate number) if prime_candidate is prime
+        prime_candidate+=2      #check odd numbers
+t1=time()
+primes=generate_primes(24)      #the primes less than 24, since the primorial needs to be less than 1e9
+pseudofortunates=set()      
+for i in admissiblenums():
+    pseudofortunates.add(pseudofortunate(i))    #adds psuedo-fortunate numbers to set
+print (sum(pseudofortunates))     #sum of unique pseudo-fortunate numbers
+t2=time()
+print t2-t1