Thread: x!^n+/-1 or x#^n+/-1? View Single Post
2020-11-13, 20:59   #8
rogue

"Mark"
Apr 2003
Between here and the

6,287 Posts

Quote:
 Originally Posted by Dylan14 Doing a quick search with pfgw with the -f1 flag, the following numbers are prime or 3-PRP for the form x!^2 +/- 1 up to x = 2000: Code: 0!^2+1 1!^2+1 2!^2+1 3!^2+1 4!^2+1 5!^2+1 9!^2+1 10!^2+1 11!^2+1 13!^2+1 24!^2+1 65!^2+1 76!^2+1 2!^2-1
I wouldn't expect anything else on the -1 side as x^n-1 always factors as (x-1) as a factor. Note that on the +1 side any primes must also be GFNs which means that n will always be a power of 2 for primes.

So from those perspectives, these forms are not that interesting.