'''
Created on 2013-01-23
@author: paymahn
'''
import CommonFunctions as cf
import time
t = time.time()
primes = cf.generate_primes_less_than(100000)
target_prime_factors = 4
target_consecutive = 4
consecutive = 0
result = 2*3*5*7
while consecutive < target_consecutive:
result += 1
if(len(cf.find_prime_factors(result, primes)) >= target_prime_factors):
consecutive+= 1
else:
consecutive = 0
print "Done executing"
print time.time() - t
print result
'''
Created on 2013-01-29
@author: paymahn
'''
'''
Use Eulers totient function:
http://www.math.okstate.edu/~wrightd/crypt/lecnotes/node18.html
'''
import CommonFunctions as cf
MAX = 10**6
totient = [0]*(MAX+1)
primes = cf.sieve_of_Erastothenes(MAX)
for i in range(2,MAX+1):
factors = cf.find_prime_factors(i, primes)
product = 1
for factor in factors:
product *= factor**factors[factor] - factor**(factors[factor]-1)
totient[i] = product
print sum(totient) * 3/7
