def main():
LIMIT = 10**6
primes = sieve_of_eratosthenes(LIMIT)
cumulative_sums = [2 for i in primes]
for i in range(1, len(cumulative_sums)):
cumulative_sums[i] = primes[i] + cumulative_sums[i-1]
result = 0
number_of_primes = 0
for i in range(0, len(cumulative_sums)):
for j in range(i - (number_of_primes + 1), -1, -1):
sum_consecutive_primes = cumulative_sums[i] - cumulative_sums[j]
# sum_consecutive_primes increases as the inner loop advances. If
# the difference is already too large, we can break the loop, since
# it will only grow larger
if sum_consecutive_primes > LIMIT:
break
if is_prime(sum_consecutive_primes):
number_of_primes = i - j
result = sum_consecutive_primes
print(result)
return
def main():
result = 0
for i in sieve_of_eratosthenes(10**6):
rotations = get_rotations(i)
if len(list(filter(lambda x : is_prime(x), rotations))) == len(rotations):
result+=1
print(result)
def main():
current_sieve_limit = 100000
sieve = sieve_of_eratosthenes(current_sieve_limit)
n = 2*3*4*5 - 1
while True:
n += 1
# Re-compute the sieve
if n > current_sieve_limit:
current_sieve_limit *= 2
sieve = sieve_of_eratosthenes(current_sieve_limit)
if (len(prime_factors(n, sieve)) == 4
and len(prime_factors(n+1, sieve)) == 4
and len(prime_factors(n+2, sieve)) == 4
and len(prime_factors(n+3, sieve)) == 4):
print(n)
break
def main():
max_run = 0
product = 0
b_set = sieve_of_eratosthenes(1000)
# With b = 2
for a in range(-998, 998, 2):
this_run = prime_run(a, 2)
if this_run > max_run:
max_run = this_run
product = a*2
# With b != 2
for a in range(-999, 999, 2):
for b in b_set[1:]:
this_run = prime_run(a, b)
if this_run > max_run:
max_run = this_run
product = a*b
print(product)
def main():
print(sum(sieve_of_eratosthenes(limit-1)))
