Another new prime (M42-Related)

[Prime95]

http://www.tomshardware.com/hardnews...27_133948.html

[akruppa]

Somebody on the Heise forum suggests to Dr. Nowak that he should use a printout of the prime for eyesight tests.

Alex

[T.Rex]

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 past, I've contributed to porting a very large 32bits application to a 64bits machine. The goal was to be able to access more than 2GB of memory, not to run faster. And I think I remember it was running slower with 64bits than with 32bits, on the same computer: a PowerPC machine.
Also, 2 years ago, I've measured performances of the IBM JVM on PowerPC. PowerPC machines can run either 32bits or 64bits instructions: very useful for comparing ! And IBM delivers 2 versions of the JVM on AIX: a 32bits JVMs and a 64bits JVM, and 2 versions of the AIX operating system: a 32bits AIX and a 64bits AIX.
Now, take an official benchmark (SPECjbb2000), run it with the 32bits JVM on the 32bits AIX, and then run it with the 64bits JVM on the 64bits AIX. Which one is the fastest ? The first one: ~10 % !! Because 64bits pointers consume more memory than 32bits pointers, which leads to caches being less efficient for the data. (And running the benchmark with the 32bits JVM on the 64bits AIX was nearly the same than with 32bits JVM on 32bits AIX.) With programs (like Java) that use pointers very often, using a 64bits machine (with the same architecture, same number of registers, ...) is slower. With HPC programs (like prime95 or GLucas), the computation (with floating-point variables) is preponderant. So I guess the performances would be the same. For floating point computation, I guess more precision leads to slower computation (number of cycles).
My conclusion: don't believe the adds. The new 64bits processors are faster than the old 32bits processors for many reasons (more registers, different architecture, more efficient pipeline, new instructions, ...), but not because of the 64bits.
I think a program built for 32bits computers can run faster on 64bits computer IF you reorganize it in depth (rewrite quite everything) in order to take profit of the 64bits for all the data the program is handling and computing. But it is not worth doing such a tremendous (and risky) task. Simply wait 18 months, and your program will run 2 times faster on the new processors !
Have a look to the new IBM processor: Cell. It's a monster.
Tony

[jinydu]

It looks like Perfectly Scientific has some work to do. They're still calling M41 a "new prime".

[jinydu]

Originally Posted by jinydu

Interestingly, Google already lists 7230 results for "42nd Mersenne Prime" but no results for 25964951.

Just hours ago, that was still the case. But now its up to 100 results:

http://www.google.com/search?hl=en&q=25964951

[garo]

George,
In the press release public is misspelt as "pubic" in one place.

[jinydu]

Originally Posted by garo

George,
In the press release public is misspelt as "pubic" in one place.

Also, the press release says:

The formula for the new prime number is 2 to the 25,964,951th power minus 1."

The use of the word "formula" seems awkward; at least I've never heard it used like this before. Also, I'm pretty sure it should be ...951st power, not ...951th power.

[Mike]

Results 1 - 10 of about 106 for 25,964,951. (0.25 seconds)

[jinydu]

Originally Posted by Mike

Results 1 - 10 of about 106 for 25,964,951. (0.25 seconds)

Hmm, many of the results don't mention it at all. I guess that by the time Google reached some sites, news of M42's discovery had already been pushed off the page. Also, most of reports seem to be copy-pastes of Slashdot's.

[edorajh]

Congratulations Dr. Nowak!

[TauCeti]

The news gains momentum in the german media. dpa features it, so i guess at least 30 local newspapers will copy the story. There is also an article on the frontpage of stern.de, one of the three largest weekly magazines in germany.

Tau