Re New test for Mersenne Primes

[K Ramsey]

I wrote a basic program that tests for Mersenne primes based on my thread "Is This of any Merit" but havn't done the task of enhancing the speed of the program yet. This program weeded out all Mersenne primes from 3 up through p = 127 correctly and checked up to p = 409 in less than 6 hours.
Starting with all the primes in column 1 of an excel spread sheet the program checks each prime in sequence and prints a one beside each prime only if 2^(p) - 1 is prime. I should be able to double the speed by using such techniques as turning off screen display etc, but have to go now.

[Uncwilly]

I fired up Dario's handy Java app. and feed it all odd exponent to 501 and it took it ~2 seconds to check all the numbers for primality.

That is 2^3-1, 2^5-1, 2^7-1,..... 2^499-1, 2^501-1

I could not find a L-L in BASIC, but, I suspect that it would kick some serious speed, FFT & DWT not included.

[K Ramsey]

Originally Posted by Uncwilly

I fired up Dario's handy Java app. and feed it all odd exponent to 501 and it took it ~2 seconds to check all the numbers for primality.

That is 2^3-1, 2^5-1, 2^7-1,..... 2^499-1, 2^501-1

I could not find a L-L in BASIC, but, I suspect that it would kick some serious speed, FFT & DWT not included.

I fed this program 2^4423 -1 and it took only about 5 seconds to print out all 1602 digits and that the number is prime! Is this really a good base mark to judge my program on?
I did improve the speed of my program a bit. It went through primes from 409 through 929 in less than 6.5 hours. I was afraid that it would take much longer so I put the numbers 521 and 607 ahead of 409 on my excel spread sheet last night to see if I didn't mess things up. I for got to remove them further down in the list so the program did these primes twice. About turning the screen update off to speed the program up, this might not applied to Excel 2003 as it was writen for Excel 97. This morning when I turned on my monitor nothing was showing beside 521 or 607 until I hit the escape button to exit the program. I was afraid at first that I screwed up and the program failed until the 1's showed up on the screen after I exited my program. I still have some improvements to make then I will trim down my program and export the module, delete it, and import it back into my workbook to see if that increases my speed. Of course all you experts out there may find this quite amusing. Are there really programs out there that can give the primeness of 2^4423 -1 on my Windows XP in less than 7 seconds without being based upon the predetermined fact of it?

[AntonVrba]

Originally Posted by K Ramsey

Are there really programs out there that can give the primeness of 2^4423 -1 on my Windows XP in less than 7 seconds without being based upon the predetermined fact of it?

YES
PFGW Version 1.2.0 for Windows [FFT v23.8]

Primality testing 2^4423-1 [N+1, Brillhart-Lehmer-Selfridge]

Running N+1 test using discriminant 3, base 1+sqrt(3)
2^4423-1 is prime! (0.1584s+0.0022s)

And 7 Seconds

PFGW Version 1.2.0 for Windows [FFT v23.8]

Primality testing 2^23209-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
2^23209-1 is prime! (7.0036s+0.0025s)

Done.

[K Ramsey]

Originally Posted by AntonVrba

YES
PFGW Version 1.2.0 for Windows [FFT v23.8]
..
Primality testing 2^23209-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
2^23209-1 is prime! (7.0036s+0.0025s)

Where do I get this program and is the code available so that I can study it?

Also since my test gives correct results for the first 162 primes excluding p=2 since 3 is a special case. Is it possible to use my conjecture and the other conjectures in this forum to give even quicker results?

[fetofs]

Originally Posted by K Ramsey

Where do I get this program and is the code available so that I can study it?

http://groups.yahoo.com/group/primeform/

The program is open-source

[troels munkner]

Sorry, your technique will never work within a reasonable span of time.
If you look on Fermat's small theorem and know more about possible primes,
you can easily find Mersenne possible primes (which embrace real MP's
and Mersenne "products")


Y.s.