Challenge: Factorize factorial numbers as product of prime numbers

Question

Create a program that receives a positive integer number and factorize the factorial of that number as a product of prime numbers. In other words, the program must receive a natural number 'n', and show the factorization as a product of prime numbers of 'n!' (factorial of 'n').

Example 1:
Input: 8
Output: 8! = 2^7 * 3^2 * 5^1 * 7^1

Example 2:
Input: 50
Output: 50! = 2^47 * 3^22 * 5^12 * 7^8 * 11^4 * 13^3 * 17^2 * 19^2 * 23^2 * 29^1 * 31^1 * 37^1 * 41^1 * 43^1 * 47^1

Example 3:
Input: 100
Output: 100! = 2^97 * 3^48 * 5^24 * 7^16 * 11^9 * 13^7 * 17^5 * 19^5 * 23^4 * 29^3 * 31^3 * 37^2 * 41^2 * 43^2 * 47^2 * 53^1 * 59^1 * 61^1 * 67^1 * 71^1 * 73^1 * 79^1 * 83^1 * 89^1 * 97^1

Factorial: https://en.wikipedia.org/wiki/Factorial
Prime number: https://en.wikipedia.org/wiki/Prime_number

Answer 1

Thank you for the beautiful challenge 👍👏
Here's my try :
https://code.sololearn.com/c1lN2W7OMsbb/?ref=app

Answer 2

Thanks for the challenge
one could do a lot of performance improvment
So the factorials of n cant be factorials of n+1
well ...here is m basic solution

https://code.sololearn.com/cCrtDXQPCvXG/?ref=app

Answer 3

my solution...
https://code.sololearn.com/cfsbdp3E1Wu5/?ref=app

Answer 4

here it is
https://code.sololearn.com/cpuatlqlEBmy/?ref=app

Answer 5

I avoided having to calculate the factorial. Hence it works for numbers even as high as 3000 and only stops on 10000 because of the time limit.

https://code.sololearn.com/cTeTGyL37QXZ/#java

Answer 6

one liner
https://code.sololearn.com/cA63OuuAS0zp/?ref=app

Answer 7

My try
https://code.sololearn.com/cbpmRDAWkMru/?ref=app

Answer 8

O(n.loglogn) complexity. Works for very large n like 20000 or higher