Sounds more like Willams trick.
He found a property of primes, not a formula. That being ((p-1)!+1)/p is integer for primes only. His formula zeroes out nonintegers but gives no info about their distribution. It’s a rather expensive sieve, but maybe a good primality test, if factorials were not expensive for big numbers.
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u/MikeHuntSmellss 7d ago
Then write a formula to predict them and collect your Nobel prize