def problem49():
primes = filter(lambda p: p >= 1000, euler.generate_primes_by_eratosthenes(10000))
prime_sets = defaultdict(list)
for prime in primes:
key = ''.join(sorted(str(prime)))
prime_sets[key].append(prime)
for k in prime_sets:
prime_set = prime_sets[k]
if len(prime_set) >= 3:
found = _test_set(prime_set)
if found is not None:
return found
raise ValueError
def problem35():
primes = euler.generate_primes_by_eratosthenes(1000000)
prime_set = set(primes)
found = 0
for prime in primes:
circular_prime = True
for x in rotate(prime):
if int(x) not in prime_set:
circular_prime = False
break
if circular_prime:
found += 1
return found
def problem46():
primes = euler.generate_primes_by_eratosthenes(MAX_VALUE)
prime_set = set(primes)
for tst in itertools.count(9, 2):
if tst > MAX_VALUE:
ValueError
if tst in prime_set:
continue
found_goldback = False
for p in primes:
if p > tst:
break
remainder = tst - p
if remainder % 2 == 0:
sqrt = math.sqrt(decimal.Decimal(remainder / 2))
if sqrt - int(sqrt) == 0:
found_goldback = True
break
if not found_goldback:
return tst
644 = 2² × 7 × 23
645 = 3 × 5 × 43
646 = 2 × 17 × 19.
Find the first four consecutive integers to have four distinct prime factors. What is the first of these numbers?
"""
import euler
import itertools
import math
MAX_VALUE = 1000000
DISTINCT = 4
primes = euler.generate_primes_by_eratosthenes(MAX_VALUE)
primes_set = set(primes)
prime_factors = {}
def find_prime_factors(value):
if value > MAX_VALUE:
raise ValueError
if value in primes_set:
return [value]
for p in primes:
if value % p == 0:
return [p] + find_prime_factors(value/p)
if p > math.sqrt(value):
break
def test_erasthonens(self):
self.assertEqual(euler.generate_primes_by_eratosthenes(10), [2, 3, 5, 7])
self.assertEqual(euler.generate_primes_by_eratosthenes(20), [2, 3, 5, 7, 11, 13, 17, 19])
import euler print sum(euler.generate_primes_by_eratosthenes(2000000))
