def solve():
n = 428571
d = 0
while True:
if (7*n+1) % 3 == 0:
d = (7*n+1) / 3
print '(n,d) = (%s,%s)' % (n, d)
break
n = n - 1
l1 = mtools.prime_factors(n)
l2 = mtools.prime_factors(d)
print l1,l2
return 'n in hcf(n,d)'
def min_product_sum_with_start(k, start):
#print 'min_product_sum_with_start(%d,%d) = ' % (k, start),
i = start
while True:
if not mtools.is_prime(i):
p, c = mtools.prime_factors(i)
#i-k + len(factors) == sum(factors)
if search_match(i, p, c, k):
#print i
return i
i = i + 1
def prime_prod(n):
p,c = mtools.prime_factors(n)
if len(p) == 1 and c[0] > 1:
return (p[0], c[0])
return None
def phi(n):
p, c = mtools.prime_factors(n)
s = n
for x in p:
s = s - s/x
return s
def primes_n(s, n):
for i in range(s, s+n):
p, num = mtools.prime_factors(i)
if len(p) != n:
return False
return True