After seeing a post on this list a few weeks ago I decided to branch out
and try a few ranges from Michael Hartley's page looking for k*2^n-1
primes. I must say there is a bit of a thrill in actually discovering a
new prime every day I run the program instead of proving two numbers a
month composite. :)
Anyway, a few curious observations I made, which surprised me:
I have 2 computers, a P2-350 and P3-500. The program executes nearly 2 1/2
times as fast on the latter as on the former with nothing else
running. Apparently the Proth code takes advantage of a lot of P3
features?
With the same version of prime95 and the same version of proth on each
computer, if you run them both at the same time, under Win2000 proth gets
a higher priority and all the processing power, while under NT4, it's the
other way round, and prime95 has to be stopped or have its
priority reduced in the ini file to not smother proth. Curious. (Why run
them both at once, you ask? If the computer is going to be on all night
anyway, it'd be idle when proth finished a range unless prime95 was ready
to take over as soon as proth was done.)
I assumed that one value of k was pretty much the same as any other as far
as execution time and the chance of finding primes. To my surprise this
turned out not to be so: On the P3-500, for "most" 650<k<750, it takes
about 5 hours for 16000<n<32000 and 12 hours for 32000<n<48000 -- but for
k=701 it took less than 2 and just over 6 hours, respectively. The
phenomenon is reproducible, doesn't seem to be an artifact of other
programs or reboots or suchlike. Any number theorists care to explain what
is special about k=701 that makes it easy to check for primality?
A fun project. Now if Michael would just put a stop to that pesky server
error I could submit a half dozen more primes to him... :)
GRB
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