[Python] Prime factorization using list comprehension in Python

How to write a function which returns a list of tuples like (ci, ki) for n such that n = c1k1 c2k2 ... ciki is a prime number?

For example: 12600 = 23 · 32 · 52 · 71

Desired output: [(2, 3), (3, 2), (5, 2), (7, 1)]

I know how to do it with while but is it possible to do it using list comprehension? Efficiency is not required in this task.

# naive function
def is_prime(n):
return n > 1 and all(n % i != 0 for i in range(2, n))

# while version
def factorization_while(n):
res = []
for i in range(1, n + 1):
if is_prime(i):
j = 0
while n % i == 0:
n = n // i
j += 1
if j != 0:
res.append((i, j))
return res

# list comprehension version
def factorization(n):
return [
(i, j) for i in range(1, n + 1) if is_prime(i) \
and n % i == 0 ... # add smth
]

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