def main(limit):
"""
Get sum of all integers which can't be expressed
as the sum of two abundant numbers
"""
primes = list(primes_upto(limit))
abundant = Abundant(limit)
print sum(i for i in range(1, limit) if not abundant.has_pair(i))
def find_prime_sequence(biggest_number):
primes = set(primes_upto(biggest_number))
primes_sorted = sorted(primes)
longest_streak = []
for i, p in enumerate(primes_sorted):
current_streak = [p]
current_sum = p
for next_p in primes_sorted[i + 1:]:
if current_sum + next_p > biggest_number:
break
current_streak.append(next_p)
current_sum = current_sum + next_p
if len(current_streak) <= len(longest_streak):
continue
if current_sum in primes:
longest_streak = current_streak[:]
return longest_streak
def __init__(self, limit):
self.limit = limit
self.primes = list(primes_upto(limit))
self.calculate_abundant_numbers()
self.calculate_pairs()
from euler_math import primes_upto
# Warning: Ugly, imperative code ahead.
# Don't do this at home kids.
# I just wanted to get the solution quickly.
# This should really be done using at least some functions.
maximum = 10000
primes = primes_upto(maximum)
primes_ordered = list(primes)
primes_set = set(primes_ordered)
for i in range(9, maximum, 2):
if i in primes_set:
# Only checking composite numbers
continue
#print i
found = False
for p in primes_ordered:
# i = p + 2*x^2 with min(x) = 1
# Therefore the upper bound
# for the prime numbers is as follows:
if p > i - 2:
break
for square_num in range(1, (i - p)/2 + 1):
if i == p + 2*square_num**2:
#print "{} = {} + 2*{}^2".format(i, p, square_num)
found = True
break
if found:
break
"""
Find the product of the coefficients, a and b,
for the quadratic expression that produces the maximum number
of primes for consecutive values of n, starting with n = 0.
"""
from euler_math import primes_upto
sieve = list(primes_upto(20000))
def is_prime(x):
return x in sieve
def consecutive_primes(a,b):
n = 0
while True:
x = n**2 + a*n + b
if is_prime(x):
yield x
n += 1
else:
break
# Tests
# print len(list(consecutive_primes(1, 41))) # 40
# print len(list(consecutive_primes(-79, 1601))) # 80
max = 0
for a in range(-1000, 1000):
for b in primes_upto(1000):
length = len(list(consecutive_primes(a,b)))