def truncatable_primes():
primes = sieve_of_erastothenes(750000)
primes_set = set(primes)
truncatable = set()
for i in primes:
if i < 10:
truncatable.add(i)
continue
if is_truncatable_prime(i, primes_set):
truncatable.add(i)
truncatable.remove(2)
truncatable.remove(3)
truncatable.remove(5)
truncatable.remove(7)
return truncatable
def concat_prime_perms():
all_primes = sieve_of_erastothenes(9999)
primes = set([i for i in all_primes if i > 999])
for i in range(3333, 1000, -1):
for j in range(1000, 9999):
hits = list()
for k in range(0, 3):
curr = j + k * i
if curr > 9999:
break
if curr in primes:
hits.append(curr)
if len(hits) >= 3 and hits[0] != 1487:
if permutations(hits):
return "".join('{0}'.format(n) for n in hits)
return "- not found -"
def most_consecutive_prime_sum(max):
primes = sieve_of_erastothenes(max)
prime_count = len(primes)
p_set = set(primes)
longest_term_count = 0
ret = 0
for i in range(prime_count):
sum = 0
term_count = 0
for j in range(i, prime_count):
sum += primes[j]
if sum > max:
break
term_count += 1
if term_count > longest_term_count and sum in p_set:
longest_term_count = term_count
ret = sum
return ret
def smallest_comp_not_sum_of_prime_and_double_square():
limit = 10000
primes = sieve_of_erastothenes(limit)
odds = []
for odd in range(3, limit, 2):
if odd in primes:
continue
found = False
for prime in primes:
if prime >= odd:
break
n = odd - prime
if is_twice_a_square(n):
found = True
break
if not found:
return odd
return -1
def circular_primes(max):
primes = sieve_of_erastothenes(max)
all_numbers = [False] * (max + 1)
for p in primes:
all_numbers[p] = True
circular_primes = []
for p in primes:
all_primes = True
for perm in permute_cyclically(str(p)):
n = int(perm)
if not all_numbers[n]:
all_primes = False
break
if all_primes:
circular_primes.append(p)
return circular_primes
def main():
n = 2000000
print ("Sum of primes below {}: {}".format(n, sum(sieve_of_erastothenes(n))))