## Re: Probable factorization of 3 consecutive 60222-digit integers

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• ... Thanks. And thanks to Chris Caldwell for maintaining The Prime Database. It contains n/2 = 38602791*2^200025-1, by Jiong Sun in 2004:
Message 1 of 5 , Sep 14, 2007
> Congrats to Jens for
> n+1 = 577849*2645749*3427009*prp60203
> at
> http://hjem.get2net.dk/jka/math/consecutive_factorizations.htm

Thanks.

And thanks to Chris Caldwell for maintaining The Prime Database.
It contains n/2 = 38602791*2^200025-1, by Jiong Sun in 2004:
http://primes.utm.edu/primes/page.php?id=69628

If x and x+1 are completely factored then 3 consecutive
factorizations are achieved if x-1, x+2 or 2x+1 can be factored.

prp60203 = (38602791*2^200026-1)/(577849*2645749*3427009)
was found with the POWMOD script command in
PFGW Version 20050213.Win_Dev (Alpha/IBDWT 'caveat utilitor')

If the product of known factors in m is f then this POWMOD can be
used to make a prp test of m/f as fast as of m when m is an optimized
form.
It reduced prp time of prp60203 from 217s with PFGW Version 1.2.0 to
78s.
This advantage is so great that I only examine known primes of form
k*2^n+-1 . All 3 candidates for prp testing can be written as
cofactors of a number which is also of the optimized form k*2^n+-1.

There is obviously no plan to prove prp60203.

--
Jens Kruse Andersen
• ... Ah, if only I could get that irrational base discrete weighted transform running under linux ... David
Message 2 of 5 , Sep 15, 2007
--- In primeform@yahoogroups.com, "Jens Kruse Andersen" <jens.k.a@...>
wrote:

> prp60203 = (38602791*2^200026-1)/(577849*2645749*3427009)
> was found with the POWMOD script command in
> PFGW Version 20050213.Win_Dev (Alpha/IBDWT 'caveat utilitor')

Ah, if only I could get that irrational base discrete
weighted transform running under linux ...

David
• ... But there was plan to improve on that probable factorization: http://hjem.get2net.dk/jka/math/consecutive_factorizations.htm ... Perhaps this trawl will
Message 3 of 5 , Sep 15, 2007
--- In primeform@yahoogroups.com, "Jens Kruse Andersen" <jens.k.a@...>
wrote:

> There is obviously no plan to prove prp60203.

But there was plan to improve on that probable factorization:

http://hjem.get2net.dk/jka/math/consecutive_factorizations.htm
> n-1 = 3^2*11*13*22091*417293*c64854

Perhaps this trawl will run, and run, making Jens
update his own k=3 record at frequent intervals?

David
• ... You mailed 18 minutes after the record was added. That was fast! The hit was prp64853 = (3045*2^215472-2)/(2*17*1151*27067*173473). Chris Chatfield found
Message 4 of 5 , Sep 15, 2007
> "Jens Kruse Andersen" wrote:
>
>> There is obviously no plan to prove prp60203.
>
> But there was plan to improve on that probable factorization:
>
> http://hjem.get2net.dk/jka/math/consecutive_factorizations.htm
>> n-1 = 3^2*11*13*22091*417293*c64854

You mailed 18 minutes after the record was added. That was fast!
The hit was prp64853 = (3045*2^215472-2)/(2*17*1151*27067*173473).
Chris Chatfield found 3045*2^215472-1 in 2005:
http://primes.utm.edu/primes/page.php?id=75494

> Perhaps this trawl will run, and run, making Jens
> update his own k=3 record at frequent intervals?

It's still running. For how long is not decided, and there are
probably only few hits left on known primes.
I don't expect to search above the ongoing twin prime search at
k*2^333333+/-1 - at least not before they actually find a twin and set
a record. By then there will also be a Chen prime record to retake...

--
Jens Kruse Andersen
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