def test_primes(primes):
lp = len(primes)
for i in range(lp):
for j in range(i+1, lp):
si = str(primes[i])
sj = str(primes[j])
if not et.is_prime(int(si + sj)):
return False
if not et.is_prime(int(sj + si)):
return False
return True
def prime_digit_replacement():
primes = et.prime_sieve(9999999)[25:]
chars = '0123456789'
for p in primes:
count = {}
for s in str(p):
if count.has_key(s):
count[s] += 1
else:
count[s] = 1
for key in count:
if count[key] > 1:
not_prime = 0
for c in chars:
sp = str(p)
np = int(sp.replace(key, c))
if len(str(np)) != len(sp):
not_prime += 1
continue
if not et.is_prime(np):
not_prime += 1
if not_prime > 3:
break
if not_prime < 3:
return p
def is_prime_sequence(n):
n2 = n**2
primes = [1, 3, 7, 9, 13, 27]
for p in primes:
if not euler_tools.is_prime(n2+p):
return False
return True
def pandigital_prime():
symbols = '1234567'
products = set()
max_prime = 0
while symbols:
current = list(symbols)
while increment_last_symbol(current, symbols):
while len(current) < len(symbols):
append_symbol(current, symbols)
if et.is_prime(int(''.join(current))):
max_prime = int(''.join(current))
if max_prime > 0:
return max_prime
symbols = symbols[:-1]
def spiral_primes():
total = 1
current = 1
current_side = 1
prime_count = 0.0
total_count = 1.0
while True:
current_side += 2
for j in range(4):
current += current_side - 1
if et.is_prime(current):
prime_count += 1
total_count += 1
if prime_count / total_count < 0.1:
break
return current_side