Hi Jeff,
I have just read your e-mail and I realised that I have made a
mistake of typing on my answer to you.
I say: << it take about 100 hundred hours on one CPU
of a SGI Origin 3400 to make a single division
of a p of 1000 billion. >>
I say: << it take about 100 hundred hours on one CPU
of a SGI Origin 3400 to make a single division
of a p of 1000 billion. >>
It's not 100 hundred hours it's 100 hours (4 days) !!
Sorry for that mistake.
Sorry for that mistake.
> What is magic about 2^63? Does it not work above
> 2^63 or you just haven't tried anything larger?
> 2^63 or you just haven't tried anything larger?
2^63 is the maximum size of the divisor, just because I have
put this number in one integer*8 variable. But it will be not
too difficult to go beyond by making modifications of my
program.
This evening I had a long phone conversation with Tony
Reix from France. I'm actually thinking about a way to
prove my theory without too much disclosure. These are
Reix from France. I'm actually thinking about a way to
prove my theory without too much disclosure. These are
the preliminary bases:
. I have a program that make very fast divisions: for a divisor
. I have a program that make very fast divisions: for a divisor
less than 2^63, I can made a single division of a Mersenne
number with p of 1000 billion (10^12) in about 100 hours on
one CPU of a SGI Origin 3400. This program is well
optimized. So I think that the <<World record>> will not
be better than a factor of 10 compare to my program.
. My test issued of my theory, for divisor less than 2^63
. My test issued of my theory, for divisor less than 2^63
take only a fraction of a second.
. One people of the GIMP association send me by mail
one file with for instance 1000 divisors he choose.
These divisors will be build with p WELL above 1 billion,
but small enought so that 2pj+1 is less than 2^60
(again for technical reasons). And I will reply a few hours
later, using only my new theory, with adding comment in
front of each of these 1000 numbers: This number cannot
divide with certainty, or this number is a potential divisor.
. On my institute I have a really very big computer power
but this power will NEVER be enought to use my division
program to make all the 1000 divisions of mersenne number
with p of the order 10 billion to 1000 billion in a few hours.
. One people of the GIMP association send me by mail
one file with for instance 1000 divisors he choose.
These divisors will be build with p WELL above 1 billion,
but small enought so that 2pj+1 is less than 2^60
(again for technical reasons). And I will reply a few hours
later, using only my new theory, with adding comment in
front of each of these 1000 numbers: This number cannot
divide with certainty, or this number is a potential divisor.
. On my institute I have a really very big computer power
but this power will NEVER be enought to use my division
program to make all the 1000 divisions of mersenne number
with p of the order 10 billion to 1000 billion in a few hours.
.The only big problem of that test, is that this person should
be of absolute confidence, because he could obtain some
clues about my theory on the basis of my answers.
I hope you have understand what I have say, because it's
a little late in belgium and my english a that time is going too
a little late in belgium and my english a that time is going too
bad...
I will try to answer precisely at your other questions tomorrow,
Regards,
Olivier
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