def compute():
maximal = 0
total = 0
# Construct lists for a and b
zeroth = functions.prime_sieve(1000)
first = [-i for i in zeroth]
first = first + zeroth
# Construct list for checking if prime
temp = functions.prime_sieve(3 * 1000 * 1000)
checking = 3 * 1000000 * [False]
for i in temp:
checking[i] = True
for a in first:
for b in zeroth:
maximum = 0
n = 0
while checking[n * n + a * n + b]:
n += 1
maximum += 1
if maximum > maximal:
maximal = maximum
total = a * b
return str(total)
def compute():
total = 0
primes = functions.prime_sieve(LIMIT)
check = [False]*LIMIT
for i in primes:
string = str(i)
length = len(string)
summation = i
for j in range(length-1):
if not check[int(string[j+1:])]:
summation = 0
break
if not check[int(string[:j-1])]:
summation = 0
break
total += summation
return str(total)
def compute():
total = 0
primes = functions.prime_sieve(UPPER_BOUND)
check = functions.prime_check(UPPER_BOUND)
maximum = 0
max_prime = 0
for i in range(len(primes)):
consecutive = 1
temp_sum = primes[i]
for j in range(i+1,len(primes)):
temp_sum += primes[j]
consecutive += 1
if temp_sum >= UPPER_BOUND:
break
if check[temp_sum] and consecutive > maximum:
maximum = consecutive
max_prime = temp_sum
return str(max_prime)
def compute():
total = 0
primes = functions.prime_sieve(LIMIT)
check = [False] * LIMIT
for i in primes:
check[i] = True
for i in primes:
string = str(i)
length = len(string)
score = 1
for i in range(length):
temp = ""
for j in range(length):
temp += string[(i + j) % length]
if not check[int(temp)]:
score = 0
break
total += score
return str(total)
def compute():
total = 0
sieve = functions.prime_sieve(int(10**4))
primes = [False] * int(10**4)
for i in sieve:
primes[i] = True
for i in sieve:
if i > 10**4 / 3:
break
if i > 1000:
for j in range(1, int(10**4 / 3)):
if primes[i + j] and primes[i + 2 * j]:
p1 = str(i)
p2 = str(i + j)
p3 = str(i + 2 * j)
if sorted(p1) == sorted(p2) and sorted(p2) == sorted(p3):
if i is not 1487:
total = p1 + p2 + p3
return str(total)
def compute():
index = 10001
n = functions.prime_upper_bound(index)
primes = functions.prime_sieve(n)
return str(primes[index - 1])
def compute():
total = 0
primes = functions.prime_sieve(NUMBER)
total = sum(primes)
return str(total)
def compute():
total = 0
sieve = functions.prime_sieve(UPPER_BOUND)
numbers = UPPER_BOUND * [0]
for i in sieve:
for j in range(0,int(math.sqrt(UPPER_BOUND)/2)):
if i + 2*j*j >= UPPER_BOUND:
break
numbers[i+2*j*j] += 1
for i in range(UPPER_BOUND):
if numbers[i] == 0 and i%2 == 1 and i > 5:
total = i
break
return str(total)
from functions import isPrime, prime_sieve
def truncatable(p):
s = str(p)
while p > 0:
if p > 2 and p % 2 == 0:
return False
p //= 10
if any(not isPrime(int(s[i:])) for i in range(0, len(s))):
return False
if any(not isPrime(int(s[:i])) for i in range(len(s), 0, -1)):
return False
return True
out = []
primes = prime_sieve(1000000)
for i in primes:
if i < 10:
continue
if truncatable(i):
out.append(i)
print(sum(out))
if len(gpf(n)) == digits:
#print(n)
nums.append(n)
if len(nums) > digits-1:
print("Length:", len(nums), n)
break
n+=1
else:
del nums[:]
n += 14-(n%10)
print(nums)
'''
base_primes = [2]
primes = set(functions.prime_sieve(10, []))-set(base_primes)
def sieve(prime_factors):
flags = [True for i in range(1,1001)]
for i in prime_factors:
l = len(flags)//i
#print(l)
flags[i::i] = [False]*(l+l%2-1) #Sets all multiples to false
return list(flags)
for p in primes:
p_factors = base_primes + [p]
rel_pr = sieve(p_factors)
print(rel_pr)
for i in range(len(rel_pr)-2):
if rel_pr[i] and rel_pr[i+1]:
if __name__ == '__main__':
import time
import functions
import sys
start = time.time()
triangle_limit = 13*10**3
max_limit = 10*4
max_triangle = (triangle_limit * (triangle_limit+1))/2
triangle_sqrt = int(max_triangle**0.5)+1
primes = functions.prime_sieve(max_triangle/2)
# print(primes)
print '{} primes, max prime: {}'.format(len(primes), max(primes))
print '{: } kbytes in primes'.format(sys.getsizeof(primes)/1000)
prime_time = time.time() - start
print '{0:.3f} ms for prime numbers'.format(1000*prime_time)
#print("prime time: ", repr(prime_time))
a = 0
for i in xrange(1, triangle_limit):
#a is the triangle number
a += i
num_of_divisors = primefactoring(a, primes)
#print '{0} - {1}, divisors: {2}'.format(i, a, num_of_divisors)
# UNSOLVED
import functions as f
primes = f.prime_sieve(10000, [])
pblts = []
for prime in primes:
subs = [prime]
for i in range(0, primes.index(prime)):
if str(primes[i]) in str(prime):
subs.append(primes[i])
if len(subs) >= 3:
pblts.append(subs)
count = {i: 0 for i in primes}
for set in pblts:
for i in range(1, len(set)):
count[set[i]] += 1
for i in count.keys():
if count[i] >= 4:
print(i, count[i])
# -*- coding: UTF-8 -*-
import functions
import time
start = time.time()
limit = 2*(10**6)
primes = functions.prime_sieve(limit)
prime_sum = sum(primes)
end = time.time() - start
print("sum of primes: " + repr(prime_sum))
print("time: " + repr(end))
from functions import phi, prime_sieve
x = 1
primes = prime_sieve(10000, [])
i = 0
while x * primes[i] <= 1000000:
x = x * primes[i]
i += 1
print(x)
from functions import phi, prime_sieve
check = 15499 / 94744
"""
for i in range(2,94744):
if i%1000 == 0:
print i/1000, "%"
if 1.0*phi(i)/(i-1) < check:
print(i)
break
"""
primes = prime_sieve(50000, output=[])
val = 1
for p in range(2, 50000):
if val > 1000000:
print "Exceeded limit"
break
#print(val)
val *= p
if 1.0 * phi(val) / (val - 1) < 0.4:
print(val)
break
