--- On Mon, 2/7/11, James Merickel <

merk7777777@...> wrote:

> A115091 in the OEIS declares there

> are no primes 613<p<10^6 such that there is a k<p

> for which p^2|k!+1 and no p<10^8 with k<1201.

I'd be surprised if it wasn't either known or trivially checkable way beyond that limit. I know I've pulled out lots of factors out of k!+1, all that needs to be done is to check that they're not double factors. I don't think I was the central resource for those factors, maybe it was redgolpe who was, I forget now.

> Three PARI/GP windows are going to easily push the first

> limit to 10^7 (or find a solution) in about 7 weeks.

> If anybody with real programming capacity is interested, it

> wouldn't require very much to put the whole problem at the

> p>10^8 level.

Just from the data I've got here, there are no squared factors of k!+/-1 for k<10000 and p<1483562771179

$ tail -n 1 factorialsmall.fac

(3233!+1)%1483562771179

$ sed -e s/$/^2/ < factorialsmall.fac | gp -q | grep '= 0'

[silence]

I have other logs of other runs, but there are gaps. That's why I don't think I was the one keeping a definitive record.

Phil

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