def findSums(N, n_0, count_self=True):
if count_self and PC.PrimeCheck(N) and N <= n_0:
yield (1)
for n in PC.primes(2, n_0 + 1):
dn = N - n
if dn > 1:
yield (sum([s for s in findSums(dn, min([dn, n]))]))
def oddComposite():
x = 9
yield(x)
while True:
x += 2
if primeCheckII.PrimeCheck(x):
continue
yield(x)
def _rotPrime(str_p):
new_str_p = str_p[1:] + str_p[0]
p_list = [int(str_p)]
while new_str_p != str_p:
if not primeCheckII.PrimeCheck(int(new_str_p)):
return (False)
p_list.append(int(new_str_p))
new_str_p = new_str_p[1:] + new_str_p[0]
return (p_list)
def findSpecialPrimes():
checked_list = []
for prime in primeCheckII.primes(1000,10000):
#print(prime)
for p in permutation([x for x in range(len(str(prime)))],len(str(prime))):
s = [str(prime)[x] for x in p]
next_prime = int("".join(s))
if len(str(next_prime)) < PRIME_LENGTH or next_prime <= prime:
continue
if primeCheckII.PrimeCheck(next_prime):
d_prime = next_prime - prime
last_prime = next_prime + d_prime
if len(str(last_prime)) != PRIME_LENGTH:
continue
if primeCheckII.PrimeCheck(last_prime):
if Counter([s for s in str(last_prime)]) == Counter(s):
if prime not in checked_list:
checked_list.append(prime)
yield([prime,next_prime,last_prime])
def _truncPrimeRight(str_p, trunc_primes):
cut_right = str_p[:-1]
if cut_right == '1' or cut_right == '9':
return (False)
if int(cut_right) not in trunc_primes:
while len(cut_right) > 0:
if not primeCheckII.PrimeCheck(int(cut_right)):
return (False)
cut_right = cut_right[:-1]
return (True)
def _truncPrimeLeft(str_p, trunc_primes):
cut_left = str_p[1:]
if cut_left == '1' or cut_left == '9':
return (False)
if int(cut_left) not in trunc_primes:
while len(cut_left) > 0:
if not primeCheckII.PrimeCheck(int(cut_left)):
return (False)
cut_left = cut_left[1:]
return (True)
def findPanPrime():
for d in range(8, 1, -1):
digits = [x for x in range(1, d)]
digits.reverse()
if sum(digits) % 3 == 0:
continue
for p in permutation(digits, len(digits)):
if p[-1] not in BAD_END_NUMS:
n = int("".join([str(x) for x in p]))
if primeCheckII.PrimeCheck(n):
return (n)
def buildNum(str_x, trunc_primes):
if len(str_x) == 0:
for num in START_NUMS:
for new_str_x in buildNum(num, trunc_primes):
yield (new_str_x)
elif len(str_x) < MAX_DIGITS:
for num in GOOD_NUMS:
if str_x[0] in GOOD_LEFT_NUMS:
new_nums = [str_x + num]
elif str_x[0] in BAD_END_NUMS and len(str_x) > 1:
new_nums = [num + str_x]
elif str_x[-1] in BAD_END_NUMS and len(str_x) > 1:
new_nums = [str_x + num]
else:
new_nums = [num + str_x, str_x + num]
for new_num in new_nums:
if primeCheckII.PrimeCheck(int(new_num)):
if _truncPrimeLeft(new_num,
trunc_primes) and _truncPrimeRight(
new_num, trunc_primes):
yield (new_num)
for new_str_x in buildNum(new_num, trunc_primes):
yield (new_str_x)
break
prime_list.append(p)
min_run_len = 22
run_len = min_run_len
prime_sum = 0
for i in range(len(prime_list)):
if prime_sum + prime_list[i] < MAX_p:
prime_sum += prime_list[i]
else:
run_len = i + 1
i = 0
run = True
run_list = []
prime_sum = 0
while run:
run_list = prime_list[i:i + run_len]
prime_sum = sum(run_list)
if prime_sum > MAX_p:
i = 0
run_len -= 1
elif primeCheckII.PrimeCheck(prime_sum):
run = False
else:
i += 1
print(i, run_len)
print(prime_sum, len(run_list), run_list)
def combinePrimes(a,b):
return(primeCheckII.PrimeCheck(int(str(a)+str(b))) and primeCheckII.PrimeCheck(int(str(b)+str(a))))
def countFractions(N):
s = N - 1
if not primeCheckII.PrimeCheck(N):
D = findDivisors(N, False, False)
s -= sum([countFractions(d) for d in D])
return (s)
TR: previousBR + size-1
TL: TR + size-1
BL: TL + size-1
BR: BL + size-1
then increase size by 2
"""
from math import sqrt
import primeCheckII
size = 1
ratio = 1.0
check_list = []
TR = TL = BL = BR = 1
prime_count = 0
while ratio >= 0.1:
size += 2
TR = BR + size - 1
TL = TR + size - 1
BL = TL + size - 1
BR = BL + size - 1
check_list = [TR, TL, BL, BR]
total = 2 * (size - 1) + 1
for x in check_list:
if primeCheckII.PrimeCheck(x):
prime_count += 1
ratio = prime_count / total
print(ratio)
print(prime_count, total, ratio, size)