def consecutiveprimes(a, b):
n = 0
while 1:
if isPrime(n**2 + a * n + b):
n += 1
else:
return n
def run():
i = 1
while 1:
n = 2 * i + 1
if isPrime(n) or checker(n):
i += 1
continue
return n
def tructprime(n): if isPrime(n): m = n % 10 ** int(log(n,10)) n = n//10 while n != 0: if isPrime(n): n = n//10 else: return False while m > 10: if isPrime(m): m = m % 10 ** int(log(m,10)) else: return False return(isPrime(m)) else: return False
from projecteuler import isPrime
counter = 1
n = 3
current = 2
while(counter < 10001):
if isPrime(n):
counter += 1
current = n
n += 2
else:
n += 2
print(current)
from projecteuler import isPrime
from itertools import permutations
primes = []
for i in range(1009, 9974):
if isPrime(i):
primes.append(i)
for i in primes:
perms = list(permutations(str(i)))
perm_primes = []
for j in perms:
k = int(j[0]) * 1000 + int(j[1]) * 100 + int(j[2]) * 10 + int(j[3])
if k in primes:
perm_primes.append(k)
if len(perm_primes) >= 3:
for l in perm_primes:
if (l + 3330 in perm_primes) & (l + 6660 in perm_primes):
print(l, l + 3330, l + 6660)
from projecteuler import isPrime
from functools import reduce
prime_sum = [2]
for i in range(3, 1000000):
if isPrime(i):
prime_sum.append(prime_sum[-1] + i)
most_consec = 21
for i in range(most_consec, len(prime_sum)):
for j in range(i - (most_consec + 1), 0, -1):
if (prime_sum[i] - prime_sum[j] > 1000000):
break
if isPrime(prime_sum[i] - prime_sum[j]):
most_consec = i - j
result = prime_sum[i] - prime_sum[j]
print(result)
#this took a long time to run, very nonoptimal
from math import sqrt
from projecteuler import isPrime
primes = [x for x in range(2, 1000000) if isPrime(x)]
non_circular_p = primes[:]
for i in primes:
l_i = list(str(i))
if len([x for x in l_i if int(x) % 2 == 0 or int(x) == 5]) > 0:
continue
else:
no_good = 0
for j in range(len(l_i) - 1):
#rotate to next number
l_i.append(l_i.pop(0))
temp = int(''.join(l_i))
if temp not in primes:
no_good = 1
break
if no_good == 0:
non_circular_p.pop(non_circular_p.index(i))
non_circular_p.pop(non_circular_p.index(2))
non_circular_p.pop(non_circular_p.index(5))
def checker(n):
for i in range(1, int(sqrt(n / 2)) + 1):
if isPrime(n - 2 * i * i):
return True
return False