def E4A():
'''Return the largest palindrome P, where p = A * B, and A, B > 100'''
ps = gen_palindromeList()
for n in ps:
pCount = Counter()
for p in gen_PrimeFactors(n):
pCount.update(p)
A, B = greatestPair(pCount)
if intlen(A) == 3 and intlen(B) == 3:
return n
def E5A(n):
'''Determing the smallest number that is evenly divided by all numbers <= n'''
def maxMerge(a, b):
for k, v in b.iteritems():
if a[k] < v:
a[k] = v
master = Counter()
x = range(2, n + 1)
for i in x:
tmp = Counter()
for p in gen_PrimeFactors(i):
tmp.update(p)
maxMerge(master, tmp)
s = 1
for k, v in master.iteritems():
s *= k**v
return s