Another new prime (M42-Related) - Page 7

Orgasmic Troll · 2005-02-26, 01:15

..can I hold off on putting up the story but update my prime list?

Primeinator · 2005-02-26, 01:15

Okay, can you explain the differences between all these different systems- i.e. the one that Tony uses, the Alpha based system, and any others that you can think of? Thanks,

-Kyle

akruppa · 2005-02-26, 08:52

Congratulations everyone!

Btw, the new prime is not part of a twin prime pair, 2^(not-yet-official-exponent)-3 is divisible by 5.

Alex

Jeff Gilchrist · 2005-02-26, 12:19

Quote:

Originally Posted by Primeinator

Okay, can you explain the differences between all these different systems- i.e. the one that Tony uses, the Alpha based system, and any others that you can think of?

There are lots of differences and it can get very technical, but I will just provide some basic highlights. To get more specific details you can check out Intel. AMD, and HP's websites for more.

First, I have no idea what machine the GIMPS user was using but there is a good chance it was an AMD Athlon/Opteron, or Intel P3/P4 processor. Those are you basic 32bit processors using x86 instructions that you find in PCs.

Tony is using a machine with Intel Intel Itanium2 processors. This is a 64bit processor using ia64 instructions and is completely different from a Pentium processor. You cannot run code compiled for an Itanium on a Pentium CPU.

I am using HP Alpha processors which are 64bit and use a RISC instruction set. These are completely different from the x86 instructions and the ia64 instructions.

The idea of using different architectures and different source code to verify the suspected prime is that it is extremely unlikely that random errors in two different machine architectures and two different types of source code would both show that an exponent is prime when it is not. So the fact that the GIMPS user and Tony both agree the exponent is prime is good enough evidence to support that. That by itself is good enough from a statistical point of view, and when my run finishes it will add even more support (I'm already half way through so I might as well finish).

Jeff.

Mike · 2005-02-26, 16:29

Congrats everyone!

Primeinator · 2005-02-26, 16:42

Okay thanks. I've heard some things about a 64bit processor vs. a 32bit processor, and I know the 64bit one is signifcantly more powerful, but just how much faster is it? (I think I heard that it doesn't increase on a regular scale, i.e. a 64bit would be 2x as fast as a 32bit, but on an exponential scale, making a 64bit 10x or <insert larger number here>x faster. Can anyone verify this?)

PrimeCruncher · 2005-02-26, 17:05

Quote:

Originally Posted by Primeinator

Okay thanks. I've heard some things about a 64bit processor vs. a 32bit processor, and I know the 64bit one is signifcantly more powerful, but just how much faster is it? (I think I heard that it doesn't increase on a regular scale, i.e. a 64bit would be 2x as fast as a 32bit, but on an exponential scale, making a 64bit 10x or <insert larger number here>x faster. Can anyone verify this?)

In the Hardware forum there is a thread on 64-bit processors and the trial factoring improvements.

Primeinator · 2005-02-26, 17:16

Thanks.

Jeff Gilchrist · 2005-02-26, 18:35

Quote:

Originally Posted by Primeinator

Okay thanks. I've heard some things about a 64bit processor vs. a 32bit processor, and I know the 64bit one is signifcantly more powerful, but just how much faster is it?

It all depends on what you are trying to do. Also don't forget that the new AMD64 and Intel P4/Xeon processors are basically 32bit processors with 64bit extensions added, where as the Itanium and Alpha processors were designed as 64bit processors from the ground up.

Jeff.

jinydu · 2005-02-26, 19:06

Quote:

Originally Posted by philmoore

This also makes George the first person to be a co-discoverer of 8 Mersenne primes! Way to go! Now on to M43!

www.mersenne.org has been updated to reflect this (although it still doesn't mention the verification).

dsouza123 · 2005-02-26, 23:59

Congratulations on the discovery of M42 !

Concerning the difference of an Opteron/Athlon 64 (AMD64)
or P4/Xeon (EMT64) versus a 32-bit x86, the pure 64 bit mode
has been streamlined and enhanced.

There are double the number of integer registers, 16 instead of 8, and
the size has doubled to 64 bits from 32 bits.
This will allow a doubling of trial factoring speed.

There are more SSE2 64-bit floating point registers.
This should add a very small increase in speed,
the major advantage is a much enhanced memory access system,
mainly on AMD64, with a different enhancement for Intel,
that should allow higher memory throughput which is crucial in the DWT transforms of the lucas lehmer test.
How much of an increase remains to be seen.

2005-02-26, 16:42	#72
Primeinator "Kyle" Feb 2005 Somewhere near M52.. 2·457 Posts	Okay thanks. I've heard some things about a 64bit processor vs. a 32bit processor, and I know the 64bit one is signifcantly more powerful, but just how much faster is it? (I think I heard that it doesn't increase on a regular scale, i.e. a 64bit would be 2x as fast as a 32bit, but on an exponential scale, making a 64bit 10x or <insert larger number here>x faster. Can anyone verify this?) Last fiddled with by Primeinator on 2005-02-26 at 16:46

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2005-02-26, 01:15	#67
Orgasmic Troll Cranksta Rap Ayatollah Jul 2003 641 Posts	..can I hold off on putting up the story but update my prime list?

2005-02-26, 08:52	#69
akruppa "Nancy" Aug 2002 Alexandria 2,467 Posts	Congratulations everyone! Btw, the new prime is not part of a twin prime pair, 2^(not-yet-official-exponent)-3 is divisible by 5. Alex

2005-02-26, 16:29	#71
Mike May 2004 Vancouver, Canada 2²×5² Posts	Congrats everyone!

2005-02-26, 17:16	#74
Primeinator "Kyle" Feb 2005 Somewhere near M52.. 2×457 Posts	Thanks.

2005-02-26, 23:59	#77
dsouza123 Sep 2002 1226₈ Posts	Congratulations on the discovery of M42 ! Concerning the difference of an Opteron/Athlon 64 (AMD64) or P4/Xeon (EMT64) versus a 32-bit x86, the pure 64 bit mode has been streamlined and enhanced. There are double the number of integer registers, 16 instead of 8, and the size has doubled to 64 bits from 32 bits. This will allow a doubling of trial factoring speed. There are more SSE2 64-bit floating point registers. This should add a very small increase in speed, the major advantage is a much enhanced memory access system, mainly on AMD64, with a different enhancement for Intel, that should allow higher memory throughput which is crucial in the DWT transforms of the lucas lehmer test. How much of an increase remains to be seen.