def factors(x,i=0):
if isprime2(x):return [x]
p = sieve(int(x**.5))
for j,prime in enumerate(p[i:]):
tmp = x%prime
if tmp==0:
tp = x//prime
print(tmp,prime)
return [prime]+factors(tp,j)
return [x]
def factors(x, i=0):
if isprime2(x): return [x]
p = sieve(int(x**.5))
for j, prime in enumerate(p[i:]):
tmp = x % prime
if tmp == 0:
tp = x // prime
print(tmp, prime)
return [prime] + factors(tp, j)
return [x]
def e133():
L, q, s = 100000, pow(10, 20), 5
for p in sieve(L)[1:]:
if pow(10, q, p) != 1: s += p
return s
def e003(num=600851475143):
p = sieve(round(num**.5))
for i in p[::-1]:
if num % i: continue
else: return i
def e003(num=600851475143):
p = sieve(round(num**.5))
for i in p[::-1]:
if num%i:continue
else:return i
def e005(top=20):
return reduce(mul,[i**(ceil(log(top)/log(i))-1) for i in sieve(top)])