def prime_cut_right(n):
if n < 10:
return is_prime(n)
cut = int(str(n)[:-1])
if is_prime(cut):
return prime_cut_right(cut)
return False
def prime_cut_left(n):
if n < 10:
return is_prime(n)
cut = int(str(n)[1:])
if is_prime(cut):
return prime_cut_left(cut)
return False
def find_largest_prime_factor(number=DEFAULT_INPUT):
if is_prime(number):
return number
largest = 1
i = 2
while i * i <= number:
if number % i == 0 and is_prime(i):
largest = i
i += 1
return largest
def compute_smallest_evenly_divisible_number(ceiling=DEFAULT_INPUT):
result = 1
i = 2
while i <= ceiling:
if is_prime(i):
powered_prime = i
while powered_prime * i <= ceiling:
powered_prime *= i
result *= powered_prime
i += 1
return result
def sum_prime_numbers_up_to_n(n=DEFAULT_INPUT):
if n < 2:
return 0
sum = 2
if n > 2:
i = 3
while i < n:
if is_prime(i):
sum += i
i += 2
return sum
def find_nth_prime_number(n=DEFAULT_INPUT):
if n == 0:
return None
if n == 1:
return 2
latest_prime = 3
if n > 2:
for _ in range(3, n + 1):
current = latest_prime + 2
while not is_prime(current):
current += 2
latest_prime = current
return latest_prime
from math import sqrt
from euler_common import is_prime
def digit_rotations(n):
s = list(str(n))
result = []
for i in range(len(s)):
s.append(s[0])
del s[0]
result.append(int(''.join(s)))
return result
count = 0
for n in range(1000000):
is_circular = True
for r in digit_rotations(n):
if not is_prime(r):
is_circular = False
break
if is_circular:
count += 1
print count
from euler_common import is_prime
best_l = best_p = 0
for a in range(-999, 1000):
for b in range(-999, 1000):
count = 0
n = 0
while n * n + a * n + b > 0 and is_prime(n * n + a * n + b):
n += 1
if n > best_l:
best_p = a * b
best_l = n
print best_p
from __future__ import print_function, division
from euler_common import is_prime
side_length = 1
end = 1
n_prime_diagonals = 0
n_diagonals = 1
while True:
side_length += 2
for _ in range(1, 5):
end += side_length - 1
n_diagonals += 1
if is_prime(end):
n_prime_diagonals += 1
if 100 * n_prime_diagonals // n_diagonals < 10:
break
print(side_length)
from euler_common import is_prime
from math import sqrt
num = 600851475143
root = sqrt(num)
i = 1
sum = []
while i < root:
i += 1
if num % i == 0:
if is_prime(i):
sum.append(i)
if is_prime(num / i):
sum.append(num / i)
print max(sum)
def prime_cut_left(n):
if n < 10:
return is_prime(n)
cut = int(str(n)[1:])
if is_prime(cut):
return prime_cut_left(cut)
return False
def prime_cut_right(n):
if n < 10:
return is_prime(n)
cut = int(str(n)[:-1])
if is_prime(cut):
return prime_cut_right(cut)
return False
n = 7 # 2, 3, 5, 7 don't count
count = 0
total = 0
# We are told only 11 exist
while count < 11:
n += 2
if is_prime(n) and prime_cut_left(n) and prime_cut_right(n):
count += 1
total += n
print total
def f(p):
for l in range(len(p), 0, -1):
for s in range(0, len(p) - l):
n = sum(p[s:s + l])
if is_prime(n):
return n
from euler_common import is_prime
n = 1 # Starts at 2, 1 added in loop
n_prime = 1
while n_prime <= 10001:
n += 1
if is_prime(n):
n_prime += 1
print n
from euler_common import is_prime
total = 0
i = 3
while i < 2000000:
if is_prime(i):
total += i
i += 2
# Add 2, 2 is the only even prime
print total + 2