- David Broadhurst wrote:
> Congrats to Jens for

Thanks.

> n+1 = 577849*2645749*3427009*prp60203

> at

> http://hjem.get2net.dk/jka/math/consecutive_factorizations.htm

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 - --- In primeform@yahoogroups.com, "Jens Kruse Andersen" <jens.k.a@...>

wrote:

> prp60203 = (38602791*2^200026-1)/(577849*2645749*3427009)

Ah, if only I could get that irrational base discrete

> was found with the POWMOD script command in

> PFGW Version 20050213.Win_Dev (Alpha/IBDWT 'caveat utilitor')

weighted transform running under linux ...

David - --- 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 - David Broadhurst wrote:
> "Jens Kruse Andersen" wrote:

You mailed 18 minutes after the record was added. That was fast!

>

>> 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

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

It's still running. For how long is not decided, and there are

> update his own k=3 record at frequent intervals?

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