> Using the power of GPUs we are able to calculate F99999999 in only 17 milliseconds on my Consumer GPU

FWIW, on my 2020 era laptop, the following:

  #include <stdio.h>
  
  int main(void) {
    int a = 1, b = 1, c, n = 99999999;
    while (--n) {
      c = (a+b) % 9837;
      a = b;
      b = c;
    }
    printf("%d\n", a);
    return 0;
  }

takes 330 ms measured as "time a.out".

The problem with Fibonacci is there are algorithmic ways to speed things up. The following (using the method at https://en.wikipedia.org/wiki/Fibonacci_sequence to compute Fibonacci numbers recursively in O(log n) arithmetic operations) takes Python 0.1 ms to compute the same value:

  import functools

  @functools.cache
  def F(n):
      if n <= 2:
          return 1

      m = n // 2 # rounds down
      if n % 2:
          # odd
          return (F(m+1)**2 + F(m)**2) % 9837
      else:
          return ((2*F(m+1) - F(m))*F(m)) % 9837

  print(F(99999999))