From: Matthew J Ghio <mg5n+@andrew.cmu.edu>

To: collins@newton.apple.com (Scott Collins)

Message Hash: d906c7c05eaca5cce0c01d7571d7c44f81b9638ac77f7af6ced01a91421f50e8

Message ID: <AheOyHC00WC0QH7kpb@andrew.cmu.edu>

Reply To: <9404111823.AA19530@newton.apple.com>

UTC Datetime: 1994-04-11 20:16:59 UTC

Raw Date: Mon, 11 Apr 94 13:16:59 PDT

```
From: Matthew J Ghio <mg5n+@andrew.cmu.edu>
Date: Mon, 11 Apr 94 13:16:59 PDT
To: collins@newton.apple.com (Scott Collins)
Subject: Re: (n!+1)^(1/2)
In-Reply-To: <9404111823.AA19530@newton.apple.com>
Message-ID: <AheOyHC00WC0QH7kpb@andrew.cmu.edu>
MIME-Version: 1.0
Content-Type: text/plain
collins@newton.apple.com (Scott Collins):
> >For any number n, if the square root of (n!)+1 is an integer, it is also
> >prime. (This is interesting, but rather useless in practice)
>
>For any number a, 1<a<=n, n! mod a == 0; therefore, n!+1 mod a == 1.
>n!+1 is prime. Prime numbers don't have integral square roots.
Well, it was quoted from memory, so it's possible that I made an error,
but it seems to work as stated...
For example :
(4!+1)^(1/2)=5
(5!+1)^(1/2)=11
(7!+1)^(1/2)=71
I can't find a value which produces a result that is a non-prime
integer. (Of course that doesn't prove that there isn't one.)
```

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- 1994-04-11 (Mon, 11 Apr 94 12:21:30 PDT) - Re: (n!+1)^(1/2) -
*collins@newton.apple.com (Scott Collins)*- 1994-04-11 (Mon, 11 Apr 94 13:16:59 PDT) - Re: (n!+1)^(1/2) -
*Matthew J Ghio <mg5n+@andrew.cmu.edu>* - 1994-04-15 (Fri, 15 Apr 94 16:19:49 PDT) - Re: (n!+1)^(1/2) -
*kafka@desert.hacktic.nl (-=[ Patrick Oonk ]=-)*

- 1994-04-11 (Mon, 11 Apr 94 13:16:59 PDT) - Re: (n!+1)^(1/2) -