import primecache
prime_list = primecache.primelist(150000)
def primefactors(num):
pf = []
i = 0
while num>1:
if num%prime_list[i]==0:
while num%prime_list[i]==0:
num/=prime_list[i]
if prime_list[i] in pf or len(pf)>0 and pf[len(pf)-1]%prime_list[i]==0:
pf[len(pf)-1] *= prime_list[i]
else:
pf.append(prime_list[i])
i += 1
else:
i += 1
return pf
notfound = True
start = 10
lim = 4
while notfound:
chain = 0
cons_prime = []
cons_prime_len = []
for i in range(start,start+lim):
pfactors = primefactors(i)
cons_prime_len.append(len(pfactors))
for j in pfactors:
cons_prime.append(j)
#print(cons_prime,cons_prime_len)
allval = 1
for i in cons_prime_len:
if i == lim:
allval *= 1
else:
allval *= 0
if allval == 1 and len(cons_prime) == len(set(cons_prime)):
print(start)
notfound = False
else:
start += 1