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Old 2020-11-13, 20:59   #8
rogue
 
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"Mark"
Apr 2003
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Quote:
Originally Posted by Dylan14 View Post
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.
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