def blankSlotPrimes(n,m):
d = n - m # d for digits
# Create list of primes we will use
primeList = pf.sieveEratosthenes(10**(n+1))
# Remove primes that are too small
startIndex = 0
for i in xrange(0,len(primeList)):
if primeList[i] > 10**(n-1):
startIndex = i
break
primeList = primeList[startIndex:]
# Set up set for fast prime checking
primeSet = set(primeList)
# Indecies for the repeated digits
digitIndeces = []
for i in xrange(0,m):
digitIndeces.append(range(0,d+1))
# Data structure cleverness - how we insert the repeated digits
# into the number
NumStruct = ['' for x in xrange(0,2*d+1)]
numIndex = [ 2*x+1 for x in xrange(0,d)]
repIndex = [ 2*x for x in xrange(0,d+1)]
# Keep track of maximum
maxPrimeCount = 0
maxPrimeStruct = ([],[])
# Go through all the numbers with the repeated digits
for ni in xrange(0,10**d):
# Set up the struct
numStr = str(ni).zfill(d)
for i in xrange(0,d):
NumStruct[numIndex[i]] = numStr[i]
# Find the repeated indecies with the most primes
for t in itertools.product(*digitIndeces):
primeCount = 0
smallestValue = -1 # Store the smallest value of the prime
# Loop through actual value of repeated digits
for r in xrange(0,10):
numStruct = list(NumStruct)
# Place in the digits according to positions, t
for i in xrange(0,len(t)):
numStruct[repIndex[t[i]]] += (str(r))
# Check if the number is prime
num = int(''.join(numStruct))
if num in primeSet:
if smallestValue < 0:
smallestValue = r # Update the smallest value of the prime
primeCount += 1
# Update maximum
if primeCount > maxPrimeCount:
maxPrimeCount = primeCount
numStruct = list(NumStruct)
for i in xrange(0,len(t)):
numStruct[repIndex[t[i]]] += str(smallestValue)
smallest = int(''.join(numStruct))
maxPrimeStruct = (list(t),list(NumStruct),smallest)
return (maxPrimeCount, maxPrimeStruct)
progress = 1503 lastprime = x while x < 10**7: if pf.isPrimeFast(x): count += 1 lastprime = x if count == 10001: # print "FOUND IT" # print (x, count) return if x % progress == 0: print (lastprime,count) x += 2 # Best solution if problem == 7: primelist = pf.sieveEratosthenes(2*10**6) print primelist[10000] ##################################################################### # Problem 8 def maxprod(nums,k): prod = 1 for i in xrange(k): prod = nums[i] m = prod i = 0 mi = i while i < len(nums) - k: if i + k > len(nums): break
