Even k's and the Sierpinski conjecture

[philmoore]

Looks like SoB has now eliminated 67322:
http://primes.utm.edu/primes/status.php

[paulunderwood]

Was this a double check?

Answering my own question: Yes

[Jean Penné]

Yes! 67322*2^7031231 = 33661*2^7031232 is prime!

Many congrats to Sturle Sunde and the Seventeen or Bust project for this discovery!

This success being the result of a double check, I should be curious to know the 64 bits residue of the first check, which was a false negative...
Has it the appearance of a random pattern? Or is it "almost zero"?

I corrected my data page :

http://jpenne.free.fr/Sierpeven/ accordingly.

Only six k values remain to be resolved by Seventeen or Bust, and only four of them : 10223, 21181, 22699, and 24737 are necessary to eliminate all the remaining even candidates, excepted 65536.

Nevertheless, my conjecture is that 65536 is an even Sierpinski number!

It could be demonstrated if somebody found a formula giving an infinite covering set for this number. Such a result would also demonstrate that there are only 5 Fermat primes...

Who wants to take up this challenge?

Regards,
Jean

[gd_barnes]

k's that are multiples of the base have now been added to the new "Conjectures 'R Us" effort in this 'Prime Search Projects' forum. That makes this a subset of the conjectures effort. If there is any additional info. related to the Sierp even-k conjecture, please report it there. There are no additional k's to search and I have made note of the special situation of GFn k=65536 on one of the web pages.

After a couple of days, I'd like to request that this thread be moved to the new project and locked to avoid any duplication of future effort. Please let me know if you have any problems with this.


Thanks,
Gary

[Jean Penné]

Originally Posted by gd_barnes

k's that are multiples of the base have now been added to the new "Conjectures 'R Us" effort in this 'Prime Search Projects' forum. That makes this a subset of the conjectures effort. If there is any additional info. related to the Sierp even-k conjecture, please report it there. There are no additional k's to search and I have made note of the special situation of GFn k=65536 on one of the web pages.

After a couple of days, I'd like to request that this thread be moved to the new project and locked to avoid any duplication of future effort. Please let me know if you have any problems with this.


Thanks,
Gary

No problem for me!
I agree with you to move this thread into "Conjectures 'R Us" as a sub project.
Regards,
Jean

[gd_barnes]

Originally Posted by Jean Penné

No problem for me!
I agree with you to move this thread into "Conjectures 'R Us" as a sub project.
Regards,
Jean

OK, I will do that shortly.

Note...Technically this will not be a subproject. It'll just be a subset of the project now that we include k's that are a multiple of the base.

But the Riesel and Sierp base 2 even-n and odd-n conjectures will be subprojects because they are something just a little different. I'll add them as such to the project description sometime this weekend.


Gary

[Jean Penné]

Originally Posted by gd_barnes

OK, I will do that shortly.

Note...Technically this will not be a subproject. It'll just be a subset of the project now that we include k's that are a multiple of the base.

But the Riesel and Sierp base 2 even-n and odd-n conjectures will be subprojects because they are something just a little different. I'll add them as such to the project description sometime this weekend.


Gary

Yes, I agree also with that ; and very probably, this problem will not be resolved before a while, if ever resolved...

Jean