def primechainsum(chains, primes):
for chain in chains:
if len(chain) == primes: return sum(chain)
return 0
# check against every prime in every array and add if applicable
n = 2 # the latest prime to be checked
ptc = 5
chains = []
primecandidates = []
tt1 = 0
while primechainsum(chains, ptc) == 0:
if n == primes[-1]: primetools.sieve(len(primes) + 1, primes, True)
n = primes[primes.index(n) + 1]
primecandidates = []
for prime in primes:
if areprime(merge(n, prime)): primecandidates.append(prime)
for chain in chains:
allmatch = True
for prime in chain:
if prime not in primecandidates:
allmatch = False
break
if allmatch: chains.append(chain + [n])
chains.append([n])
from primetools import sieve
from time import time
phi2 = lambda p1, p2: p1 * p2 - (p1 + p2 - 1)
primes = [2,3]
limit = 10**7
st = time()
sieve(limit ** (1/2) * 1.5, primes)
first = 0
minrat = 0
minratn = 0
for p1 in range(len(primes)):
if primes[p1] ** 2 < limit: continue
if first == 0: first = p1
for p2 in range(first, -1, -1):
t = primes[p1] * primes[p2]
if t > limit: continue
p = phi2(primes[p1], primes[p2])
if t / p > minrat and minrat > 0: break
if sorted(str(p)) == sorted(str(t)):
minrat = t/p
minratn = t
break
print(minratn)
print(time() - st)
