--- Leonid Durman <

durman@...> wrote:

> Hello all,

>

> I have made small researches for page.

> Strong PRPs

> http://www.utm.edu//research/primes/prove/prove2_3.html

>

> I checked only two bases what to detect the best values for "Combining these

> tests to prove primality".

>

> Chris Caldwell write:

> > If n < 9,080,191 is a both 31 and 73-SPRP, then n is prime.

>

> checked a1<109, a2< 7919 and other values are retrieved:

> If n < 9,254,521 is a both 103 and 6871-SPRP, then n is prime.

> If n < 9,863,461 is a both 17 and 6661-SPRP, then n is prime.

> and best

> If n < 18,985,627 is a both 31 and 1171 -SPRP, then n is prime.

>

> Who more densely researched Combining tests for 2,3,4 ... values? More than

> it is known on page Chris.

> You see the knowledge of these numbers has practical value and to success

> competes with the sieve of Eratosthenes with small numbers, for the daily

> tests, because not enough memory requires.

Great work, Leonid.

I briefly looked at this problem in the past, but I restricted myself to a

smaller set of bases, and discovered that I was almost certainly just

treading over ground covered by Jaeschke already.

Am I right in thinking that your a1/a2 distinction was to first find a1-SPSPs

for all a1 in range, and then only check a2-SPSP-ness for this restricted

set of candidates?

This looks like it's screaming for some distributed computing effort...

With a massively parallel modular multiplier/exponentiator such as Jim's or David's

from their GFNSieve, it might be possible to push this a lot further.

I'd happily stick my PPro/200 on this 24/7 for many a month, as it's doing

nothing else presently (I know - it's a crime against primality).

It looks like it can be distributed easily, as it's can be turned into a

2D-task (which means it's easy to make sure people don't tread on each

other's toes, and can still run as long as they want).

Phil

=====

"The hottest places in Hell are reserved for those who, in

times of moral crisis, preserved their neutrality."

-- John F. Kennedy, 24 June 1963, claiming to quote Dante,

to whom this has been incorrectly attributed ever since.

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