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• Moving away from prime quadruples, there is another topic that I have never seen anything written about that I am curious about. I know from tables of
Message 1 of 5 , Nov 29, 2003
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Moving away from prime quadruples, there is another topic that I have

I know from tables of generalised repunit primes that ((n^n)-1)/(n-1)
is prime for n = 2, 3, 19 and 31 and for no other n up to 1,000. Is
there a theorem that could show these four numbers to be the only n for
which ((n^n)-1)/(n-1) is prime?

Also, when was the primality of 19^19-1/18 and 31^31-1/30 proved? [I am
curious]
• I have worked on these at the same time I worked on 2*a^a+-1. N must be prime in order for the above to be prime. I have searched for PRP s for a large n value
Message 1 of 5 , Nov 29, 2003
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I have worked on these at the same time I worked on 2*a^a+-1. N must
be prime in order for the above to be prime. I have searched for
PRP's for a large n value (above 10000) and found only these 4.
Probably the number of primes of this type are finite.
As for n=13 and 19, both are prime.

Harsh Aggarwal

wrote:
> Moving away from prime quadruples, there is another topic that I
have
>
> I know from tables of generalised repunit primes that ((n^n)-1)/(n-
1)
> is prime for n = 2, 3, 19 and 31 and for no other n up to 1,000. Is
> there a theorem that could show these four numbers to be the only n
for
> which ((n^n)-1)/(n-1) is prime?
>
> Also, when was the primality of 19^19-1/18 and 31^31-1/30 proved?
[I am
> curious]
• The best way to search for these is use PFGW and use phi(\$a,\$a) in the ABC2 file . and select a: primes from 1 to 10000. --Harsh ... have ... 1) ... for ... [I
Message 1 of 5 , Nov 29, 2003
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The best way to search for these is use PFGW and use phi(\$a,\$a) in
the ABC2 file . and select a: primes from 1 to 10000.

--Harsh

wrote:
> Moving away from prime quadruples, there is another topic that I
have
>
> I know from tables of generalised repunit primes that ((n^n)-1)/(n-
1)
> is prime for n = 2, 3, 19 and 31 and for no other n up to 1,000. Is
> there a theorem that could show these four numbers to be the only n
for
> which ((n^n)-1)/(n-1) is prime?
>
> Also, when was the primality of 19^19-1/18 and 31^31-1/30 proved?
[I am
> curious]
• ... have ... ((n^n)-1)/(n-1) ... for ... [I am ... The next value of n that yields a probable prime is 7547. See sequence A088790 has more information. Tony
Message 1 of 5 , Nov 30, 2003
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wrote:
> Moving away from prime quadruples, there is another topic that I
have
>
> I know from tables of generalised repunit primes that
((n^n)-1)/(n-1)
> is prime for n = 2, 3, 19 and 31 and for no other n up to 1,000. Is
> there a theorem that could show these four numbers to be the only n
for
> which ((n^n)-1)/(n-1) is prime?
>
> Also, when was the primality of 19^19-1/18 and 31^31-1/30 proved?
[I am
> curious]

The next value of n that yields a probable prime is 7547. See

Tony
• It din t show up when I ran PFGW. Makes me wonder what base did I use, or was there an error during the process if P7547 is actually prime. Harsh Aggarwal
Message 1 of 5 , Nov 30, 2003
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It din't show up when I ran PFGW. Makes me wonder what base did I
use, or was there an error during the process if P7547 is actually
prime.

Harsh Aggarwal

>
> The next value of n that yields a probable prime is 7547. See