Juicy highly composite number needs factorization

[kevolegend]

Trawling the interwebs, I have stumbled across a 101 digit highly composite number. It's a beast to say to least

10334475851656087128243643125471284565310588797552748096314114788137761206785997576812685774304768000

Online websites only calculate up to 64 digits maximum

I am wanting it's factorization in order to work out it's number of divisors and to simply grasp the structure/patterns behind large highly composite numbers

After a little debugging, I managed to get this program working:-

# Python program to print prime factors 
  
import math  
# A function to print all prime factors of  
# a given number n 
def primeFactors(n): 
      
    # Print the number of two's that divide n 
    while n % 2 == 0: 
        print (2,end="") 
        n = n / 2
          
    # n must be odd at this point 
    # so a skip of 2 ( i = i + 2) can be used 
    for i in range(3,int(math.sqrt(n))+1,2): 
          
        # while i divides n , print i ad divide n 
        while n % i== 0: 
            print (i,end=""), 
            n = n / i 
              
    # Condition if n is a prime 
    # number greater than 2 
    if n > 2: 
        print (n) 
          
# Driver Program to test above function 
  
n = 10334475851656087128243643125471284565310588797552748096314114788137761206785997576812685774304768000

primeFactors(n) 
  
# This code is contributed by Harshit Agrawal

https://www.geeksforgeeks.org/print-all-prime-factors-of-a-given-number/

result was:-

2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222871414146316299.0

Which i worked out as: 2^283 and whatever 871414146316299.0 means

This does not seem correct. The biggest highly composite number calculable on number empire is
https://www.numberempire.com/963761198400

Which follows this factorization pattern

2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3 * 3 * 5 * 5
2^6 * 3^4 * 5^2
sextuplet, quartet, duo

Then simply "nails" the subsequent "lone prime" numbers in prime number sequence, doubling the divisor count of 105 from integer 129600 every new "lone prime"

Lone prime meaning to no power (no exponent) in the factorization

https://www.numberempire.com/129600

64 tetrahedron grid noticed which is pretty neat(2^6=64)

Thanks all,
Kev