How many ways we can represent 50! as the sum of two primes?

[hadi amiri 4]

in how many ways we can represent 50! as the sum of two primes?

 

[huba]

Are you looking for a number, an approximation, a formula, or an algorithm?
A062311, in the Encyclopedia of Integer Sequences, lists the first 13 "number of ways writing n! as a sum of two primes", that is it goes as far as 13!, it does not have a formula for a "reasonable" calculation by hand, and the last 5 terms were added as recently as 2008! (my last ! is an exclamation mark)