def quadratic_primes(number):
prime = c.prime_list_generator(number, False)
max_len = 0
for a in range(3, prime[-1], 2):
for b in prime:
max_len = max_quad_prime_series(max_len, a, b)
max_len = max_quad_prime_series(max_len, a, -b)
max_len = max_quad_prime_series(max_len, -a, b)
max_len = max_quad_prime_series(max_len, -a, -b)
def consequtive_prime_sum(max=100):
import sys
sys.path.append('../')
import common as c
primes_bool = c.prime_list_generator(
max) # [False, False, True, True, False, ...]
primes = c.prime_list_generator(max, False) # [2, 3, 5, 7, 11, ...]
start, len_max, max_sum = 0, 0, 0 # where the results are stored
for i in range(len(primes)):
sum = primes[i] # initialize sum
for j in range(i + 1, len(primes)):
sum += primes[j]
if (sum < max): # if sum is out of range, skip the larger primes
if (primes_bool[sum]): # if 2nd conditional also met...
l = j - i + 1 # calculate length of the series
if (l > len_max):
len_max, start, max_sum = l, primes[i], sum
else:
break
print("start = ", start, " :: ", "max = ", len_max, " :: ", "sum = ",
max_sum)
def truncatable_primes(max, start=23):
import sys
sys.path.append('../')
import common as c
primes = c.prime_list_generator(max)
sum, my_list = 0, []
for i in range(start, max):
if primes[i]:
# initialize left with the number, right with 0, and multiplier of 1
(left, right, mul, ok) = (i, 0, 1, True)
while (ok and left > 0):
right += (left % 10) * mul # grow the right number
ok = primes[right] and primes[left] # check for primeness for early exit
mul *= 10 # increase multiplier
left = int(left / 10) # shrink the left number
if ok: # is it a truncatable prime?
sum += i
my_list.append(i)
print("sum = ", sum, "len = ", len(my_list), my_list)
def prime_permutations(digits=4):
import sys
sys.path.append('../')
import common as c
max = 10**digits
primes_bool = c.prime_list_generator(max)
primes = [
x for x in range((10**(digits - 1) - 1), 10**digits) if primes_bool[x]
]
for i in range(len(primes)):
for j in range(i + 1, len(primes)):
next_j = 2 * primes[j] - primes[
i] # C = B + diff ; where diff = B - A
if (next_j > max): break
if (primes_bool[next_j]): # check for condition #3, (and 2)
i_list = sorted(str(primes[i]))
j_list = sorted(str(primes[j]))
n_list = sorted(str(next_j))
if ((i_list == j_list) and (j_list == n_list)): # condition #1
print("diff = ", "{:7d}".format(primes[j] - primes[i]),
" :: ", primes[i], primes[j], next_j)
'''
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all prime numbers below 2,000,000
'''
import time # get a sense of the time taken
t = time.time() # get time just before the main routine
########## the main routine #############
import sys
sys.path.append('../')
import common as c
number = 2000000
print("sum of primes = ", sum(c.prime_list_generator(number, False)))
########## end of main routine ###########
t = time.time() - t # and now, after the routine
print("time = {:7.5f} s\t{:7.5f} ms\t{:7.3f} µs".format(
t, t * 1000, t * 1000000))