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Old 2006-02-04, 12:21   #1
robert44444uk
 
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Jun 2003
Oxford, UK

77216 Posts
Default Largest Simultaneous Primes

I have been in correspondence with Jens Kruse Andersen, who maintains the records for simultaneous primes, with a view of accepting the Octoproth forms into the record books.

His response, quoted with his permission:

"There are several things I would like before allowing your forms (less might
do in some cases):

A set of simultaneous primes should be uniquely determined from one of the
primes and its position in the set.
I think there might be different octoproth (n,k) pairs with the same starting
prime 2^n-k.
I think the limitation k<2^(n-1) would prevent such situations in a reasonable
way.
Am I right?
I am not asking you to change your definition, only to accept a limitation in
which sets can be listed at my site.

http://hjem.get2net.dk/jka/math/simultprime.htm names the type in the tables.
A common 4?/8/12/16/? name, e.g. "multiproth", would be nice for reference.
Have you considered 4-sets (2^n+-k, k*2^n+-1) ?

The currently allowed forms have a maintained record page which is linked from
my page.
Such a multiproth page would be good for easy comparison.
It only needs to keep the single largest case for each number of primes.

The nth of 2n primes in a set counts for size in comparison to other
constellation types. Multiproths get a disadvantage because the largest n
primes are considerably larger. You must accept this handicap. I don't want to
credit a size where almost all prp tests in the search were on significantly
smaller numbers."

So I think we have a chance here to qualify as we restrict the 2^n-k form.

I cannot get onto his site at present - I am timed out - to find out what the records are for 8- 12- and 16- and we are at a disadvantage as mentioned above, but maybe we should be trying for these records? What do people think?

Regards

Robert Smith

Last fiddled with by robert44444uk on 2006-02-04 at 12:23
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