PRP in A138957
 

There were some posts about [url]https://oeis.org/A007908[/url], so in case
someone is interested in [url]https://oeis.org/A138957[/url] too: I got the
7816th term PRP, 30157 digits. It would be nice if someone could doublecheck.
I went up to 39999 without another hit, so no other PRPs up to 70K-th term.

Attach the decimal expansion in a file and I will check it out for you. :smile:

[QUOTE=paulunderwood;430891]Attach the decimal expansion in a file and I will check it out for you. :smile:[/QUOTE]
In case I messed up somewhere, does testing my file
qualify as valid doublecheck? :smile:

For each a in {0,3,4,5,6,7} jacobiSymbol(a^2-4,n)==-1 and (x+a)^(n+1)==5+2*a (mod n, x^2-a*x+1)., which implies Euler-PRP tests base 5+2*a and associated Lucas PRP tests.

Congrats on something that is almost certainly prime, modulo an ECPP check.

Maybe you missed a PRP .... :wink:

What I meant is, yes, the number in the file is a PRP, but is it the 'right' number?
For instance, bug in my string generation. A doublechecker should use its own.

[CODE]? v=[];for(n=1,7816,d=digits(n);forstep(k=#d,1,-1,v=concat(v,d[k])));JF=read("../../Downloads/7816-30157digits.txt");digits(JF)==v
1
[/CODE]

:tu:

Thanks!

[QUOTE=paulunderwood;430903](x+a)^(n+1)==5+2*a (mod n, x^2-a*x+1)., [/QUOTE]

Should have said: (x+2)^(n+1)==5+2*a (mod n, x^2-a*x+1)

[QUOTE=paulunderwood;430903]
Congrats on something that is almost certainly prime, modulo an ECPP check.

[/QUOTE]

Are large PRPs of any value/interest?
If so what sizes would be interesting?

Thank you in advance.

BTW that thread seems to be here:
[url]http://www.mersenneforum.org/showthread.php?p=415695#post415695[/url]

[QUOTE=a1call;430926]Are large PRPs of any value/interest?
If so what sizes would be interesting?[/QUOTE]

No particular value afaik, but if they're larger than 41169 digits they are large enough to make Henri Lifchitz & Renaud Lifchitz's [url=http://www.primenumbers.net/prptop/prptop.php]PRP Records[/url] page.

[url]http://www.primenumbers.net/prptop/prptop.php?page=40#haut[/url]

You can enter "page" beyond "40", so that the actual lower limit is now 20k digits for submissions. :smile:

By summing periodic digits, one can obtain an algebraic form for this number.
It will be relatively short.

Thank you [B]CRGreathouse [/B]for the link


[QUOTE=paulunderwood;430968][url]http://www.primenumbers.net/prptop/prptop.php?page=40#haut[/url]

You can enter "page" beyond "40", so that the actual lower limit is now 20k digits for submissions. :smile:[/QUOTE]

Thank you [B]CRGreathouse [/B]for the link.

That would make to OP eligible, wouldn't it?:surprised:

I have 20K+ PRP's of my own to submit, but what's the point of asking for a minimum of 20k , when 10kth rank is 40K+?:exclaim:

And why not have an input for expanded digits like the top 5000 Primes.

[QUOTE=a1call;430997]I have 20K+ PRP's of my own to submit, but what's the point of asking for a minimum of 20k , when 10kth rank is 40K+?:exclaim:

And why not have an input for expanded digits like the top 5000 Primes.[/QUOTE]
First of all, you can look at any page. Just type the page number in the URL, e.g. here is [URL="http://www.primenumbers.net/prptop/prptop.php?page=150#haut"]page 150[/URL]

Second, most people use PRPtop not for boasting that they have a PRP on page 77, but to do cross-sectional search. For example, I know many x^y+y^x (PR)primes, but are there and x^y-y^x (PR)primes? Of course, yes, the whole [URL="http://www.primenumbers.net/prptop/searchform.php?form=x^y-y^x&action=Search"]1000+ a few of them[/URL]!
How about some multiply-and-add primes, say looking like "(((((?+3?)?" - [URL="http://www.primenumbers.net/prptop/searchform.php?form=%28%28%28%28%28%3F%2B3%3F%29%3F&action=Search"]yes, there are these, too[/URL].

Thank you for the insight, [B]Batalov[/B].


[QUOTE=Batalov;430998]How about some multiply-and-add primes, say looking like "(((((?+3?)?" - [URL="http://www.primenumbers.net/prptop/searchform.php?form=%28%28%28%28%28%3F%2B3%3F%29%3F&action=Search"]yes, there are these, too[/URL].[/QUOTE]
Now you know, I like those.:smile: