def lcm_n(n):
if n == 2:
return 2
prev_lcm = lcm_n(n-1)
prev_factors = fns.generate_prime_factors(prev_lcm)
new_factors = fns.generate_prime_factors(n)
fact_prod = fact_diff(prev_factors, new_factors)
return fact_prod * prev_lcm
series = [0, 1]
while max(series) < limit:
series.append(sum(series[-2:]))
return series[:-1]
fib_series = fib_limit(limit)
output = sum([i for i in fib_series if (i % 2 == 0)])
print "Euler 2:", output,
print "T:", time() - start; start = time()
# 3. prime factorization
import math
num = 600851475143
prime_factors = fns.generate_prime_factors(num)
print "Euler 3:", max(prime_factors),
print "T:", time() - start; start = time()
# 4. Largest palindrome
num_range = range(900, 1000)
def is_palindrome(num):
return str(num) == str(num)[::-1]
all_palindromes = []
for i in num_range:
for j in num_range:
product = i * j
print "Euler 49:", spc_list,
print "T:", time.time() - start; start = time.time()
nmax = 1000; tot = 0
for i in xrange(1, nmax + 1):
tot += i ** i
print "Euler 48:", str(tot)[-10:],
print "T:", time.time() - start; start = time.time()
nmax = 1000000; jmax = 4; i = 10
while i < nmax:
prime_facts = [len(set(fns.generate_prime_factors(x))) == jmax for x in xrange(i - jmax, i)]
if all(prime_facts):
break
i += 1
print "Euler 47:", i - jmax,
print "T:", time.time() - start; start = time.time()
def find_odd_comps(nmax):
all_comps = []
for i in xrange(3, nmax, 2):
if(not fns.is_prime(i)):
all_comps.append(i)
return all_comps
nmax = 10000
