def prime_run(a, b):
for n in xrange(100):
p = math.pow(n, 2) + a*n + b
if p > 0 and isprime(p):
continue
else:
return n
def main():
sum = 0
for n in xrange(2, 2000000+1):
if isprime(n):
sum += n
print sum
def distinct_prime_factor_count(n):
f = factors(n) - set([1, n])
prime_factors = set([])
for p in f:
if isprime(p):
prime_factors.add(p)
return len(prime_factors)
def prime_factors(n):
ret = []
for x in xrange(1, int(n**0.5) + 1):
if (n % x == 0):
if isprime(x):
print ret
ret.append(x)
return ret
def __next__(self):
while True:
self.n += 1
if self.n == 1:
self.prime = self.n
return self.prime
if self.n <= self.max:
if isprime(self.n):
self.prime = self.n
return self.prime
raise StopIteration
def truncatable_prime(n, truncate_fn):
N = str(n)
original_n = N
while True:
if isprime(int(N)):
if len(N) == 1:
return True
else:
N = str(truncate_fn(N))
else:
return False
def main(n):
primes = []
for x in xrange(2, 2*int(n*log(n))):
if isprime(x):
primes.append(x)
if len(primes) == n:
print primes
return primes[-1]
def isCircularPrime(n):
all_rotations = []
all_rotations.append(n)
for i in xrange(len(str(n))-1):
all_rotations.append(rotate_number(all_rotations[i]))
for num in all_rotations:
if not isprime(int(num)):
return False
return True
def isPandigital(n):
number = ""
for i in range(1, n+1):
number += str(i)
perms = permutations(number)
primes = []
for perm in perms:
if isprime(int(perm)):
primes.append(int(perm))
return primes
#! /usr/bin/env python
from common import isprime, permutations
primes = []
for n in xrange(1000, 10000):
if isprime(n):
primes.append(n)
primelist = {}
for prime in primes:
string_perms = set(permutations(str(prime)))
perms = []
for perm in string_perms:
p = int(perm)
if p > prime and isprime(p):
perms.append(p)
if len(perms) > 1:
perms.sort()
for perm_prime in perms:
next_prime = perm_prime + perm_prime - prime
if next_prime in perms:
print prime, perm_prime, next_prime, "- all terms concatenated:", str(prime) + str(perm_prime) + str(next_prime)
#! /usr/bin/env python3
from common import isprime
primes = [n for n in range(1000000) if isprime(n)]
longest_subset_length = 0
for p in primes[-1000:]:
# subset starts at the first prime and grows
min = 0
max = min + 1
current_sum = sum(primes[min:max+1])
while min < max:
if current_sum < p:
# grow subset with larger primes
max += 1
current_sum += primes[max]
elif current_sum > p:
# shrink subset by removing the lowest primes
min += 1
current_sum -= primes[min-1]
else:
# found the subset
subset_len = len(primes[min:max+1])
if subset_len > longest_subset_length:
longest_subset_length = subset_len
print("prime =", p, "number of terms =", subset_len)
break
#! /usr/bin/env python3
from common import isprime
primes = [n for n in range(1000000) if isprime(n)]
max_subset_length = 0
for min, p1 in enumerate(primes):
for max, p2 in enumerate(primes[min:]):
subset = primes[min:max]
prime_sum = sum(subset)
if prime_sum < 1000000 and isprime(prime_sum):
if len(subset) > max_subset_length:
max_subset_length = len(subset)
print(prime_sum, max_subset_length, p1, p2)
#! /usr/bin/env python
from common import isprime
import math
MAX = 10000
primes = []
for n in xrange(MAX):
if isprime(n):
primes.append(n)
def prime_and_twice_sqaure(n):
for p in primes:
if n <= p:
return False
for x in xrange(int(math.sqrt((n-p)/2)) + 1):
if n == p + 2 * x**2:
#print n, "=", p, "+ 2 x", x, "^2"
return True
return False
odd_composites = []
for n in xrange(1, MAX):
i = 2*n + 1
if i not in primes:
odd_composites.append(i)
for c in odd_composites:
#! /usr/bin/env python
from common import permutations, isprime
n = '0123456789'
perms = permutations(n)
primes = []
for p in range(1, 18):
if isprime(p):
primes.append(p)
def subStringDivisibility(n):
for d in range(1, 8):
if int(n[d:d+3]) % primes[d-1] != 0:
return False
return True
count = 0
sum = 0
for perm in perms:
if subStringDivisibility(perm):
count += 1
sum += int(perm)
print "the sum of all 0 to 9 pandigital numbers with this property", sum
print "count", count
