def main():
limit = 1000
primes = [2]
while primes[-1] < limit:
primes.append(get_next_prime(primes[-1]))
seqb = primes[:-1]
best = ((0, 0), 0)
for b in seqb:
if b == 2:
seqa = [i for i in range(-limit + 1, limit) if i % 2 == 0]
else:
seqa = [i for i in range(-limit, limit + 1) if i % 2 == 1]
for a in seqa:
count = 0
n = 0
while True:
if isprime(n ** 2 + a * n + b):
count += 1
if count > best[1]:
best = ((a, b), n)
n += 1
else:
break
print(best, best[0][0] * best[0][1])
def main():
width = 5
primes = 3
num = 13
while primes / ((width // 2) * 4 + 1) > 0.10:
for _ in range(3):
if isprime(num):
primes += 1
num += width - 1
width += 2
num += width - 1
print('Spiral side length:', width)
print('Primes on diagonal:', primes)
def main():
counter = 0
for n in range(2, 10 ** 6):
if all([isprime(r) for r in rotate(n)]):
counter += 1
print(n, counter)
def main():
total = 0
for n in range(10, 10**6):
if all([isprime(p) for p in truncate(n)]):
total += n
print(n, total)
def main():
i = 3
while isprime(i) or iscounter(i):
i += 2
print(i)
def main():
for l in range(9, 0, -1):
for p in generate_pandigitals(l):
if isprime(p):
print(p)
break
def get_next_prime(num):
while not isprime(num + 1):
num += 1
return num + 1