def isCircuPrime(num, digitcount):
if not isprime(num):
return False
for iteration in range(digitcount - 1):
num *= 10
num += num // (10**digitcount)
num %= 10**digitcount
if not isprime(num):
return False
return True
def solve():
for digit_count in range(7, 0, -1):
for perm_raw in permutations("7654321"[digit_count - 7:]):
num = int(''.join(perm_raw))
if isprime(num):
return num
print("Error: No pandigital primes found.")
def solve():
primes = primesbelow(33)
for odd in count(35, 2):
if isprime(odd):
primes.append(odd)
continue
for prime in primes:
if sqrt((odd - prime) // 2) % 1 == 0:
break
else:
return odd
def primefactors(num):
result = []
iterator = 2
while num > 1:
if isprime(iterator):
if num % iterator == 0:
result.append(iterator)
while num % iterator == 0:
num //= iterator
iterator += 1
return result
def factorization(num):
result = []
iterator = 2
while num > 1:
if isprime(iterator):
while num % iterator == 0:
result.append(iterator)
num //= iterator
iterator += 1
result.sort()
return result
def factorizationpow(num):
result = dict()
iterator = 2
while num > 1:
if isprime(iterator):
power = 0
while num % iterator == 0:
num //= iterator
power += 1
result[iterator] = power
iterator += 1
return result
def solve(cap=1000):
b_list = primesbelow(cap) # b must be prime (consider n = 0)
longest_streak = 0
result = 0
for a in range(-cap, cap + 1):
for b in b_list:
n = 1
while isprime(n**2 + a * n + b):
n += 1
if n - 1 > longest_streak:
longest_streak = n - 1
result = a * b
return result