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Xentar 2009-10-08 21:18

Boooooooom!!

122*18^292318+1 is 3-PRP!
[url]http://primes.utm.edu/primes/page.php?id=90343[/url]

NO k remaining for Sierp b18!
Target destroyed! :bounce: :curtisc: :george: :joe o:

Theoratically, because: I still have k=18 and k=324 on my list, but I was told, that it is not necessary to test them, because k = base. Is this still correct?


I think, this are 2-3 extra beer this weekend :smile:

MyDogBuster 2009-10-08 21:33

[QUOTE]122*18^292318+1 is 3-PRP!
[URL]http://primes.utm.edu/primes/page.php?id=90343[/URL][/QUOTE]

This is turning into an epidemic. Nice work all.:party:

gd_barnes 2009-10-08 21:36

[quote=Xentar;192263]Boooooooom!!

122*18^292318+1 is 3-PRP!
[URL]http://primes.utm.edu/primes/page.php?id=90343[/URL]

NO k remaining for Sierp b18!
Target destroyed! :bounce: :curtisc: :george: :joe o:

Theoratically, because: I still have k=18 and k=324 on my list, but I was told, that it is not necessary to test them, because k = base. Is this still correct?


I think, this are 2-3 extra beer this weekend :smile:[/quote]


YES!! A tremendous prime and it is the largest prime EVER to prove a base eclipsing Rogue's Sierp base 11 prime by a moderate margin. It is also CRUS's largest prime to date narrowly edging out Chris's recent Riesel base 6 prime...that is until Serge submits his recent Riesel base 6 prime.

In a span of 5 days, CRUS has found its 3 largest primes, all in excess of 350,000 digits and all in order of size within 20,000 digits of each other. So technically we broke our own size record 3 times.

Congratulations Daniel on a tremendous effort and proof.


:george::george::george::george::george:


To make it mathematically "official", within the next 2-3 weeks, I'll construct a list of all primes for all proven bases where the final prime was n>10K.

Prof. Caldwell will be extremely happy to hear of all of these Sierp conjecture proofs for bases <= 100. Iirc, we've now proven Sierp bases 18, 57, and 99 over the last 2-3 weeks. His published math paper dealt with all Sierp bases <= 100. After an extremely long drought on proving any of them, we've taken out 3 in short order!

Congrats again to Chris, Serge, and Daniel on recent huge CRUS primes!

Daniel, you are correct. k=18 and 324 do not need a prime because they are generalized fermat #'s (GFNs). Because they are powers of the base, they could only possibly be prime for n equal to a power of 2...i.e. n=1, 2, 4, 8, 16, 32, 64, 128, etc. and most mathematicians agree that the # of primes of GFNs is finite unlike other forms where we believe that the # of primes should be infinite, even if we haven't found a prime up to a high limit just yet. k=1 is also a GFN but it just so happens to have a prime at n=1, i.e. the value of 19.

One more thing on GFNs: Note how they differ from multiples of the base, i.e. k=36, 54, 72, etc. Multiples of the base need an n>=1 prime unless they are a GFN.


Gary

Flatlander 2009-10-08 21:52

[QUOTE=Xentar;192263]Boooooooom!!

122*18^292318+1 is 3-PRP!

Target destroyed! :bounce: :curtisc: :george: :joe o:
[/QUOTE]
Congratulations! I thought I heard a loud noise.
We're going to have to ask for more smilies! lol

Mini-Geek 2009-10-08 21:56

Congrats on the huge prime!
:george::cheesehead::party:
[quote=gd_barnes;192266] Congra[U][B]d[/B][/U]ulations Daniel [/quote]
:iws:
:judge::judge:
[quote=gd_barnes;192266] Iirc, we've now proven Sierp bases 18, 57, and 99 over the last 2-3 weeks. His published math paper dealt with all Sierp bases <= 100. After an extremely long drought on proving any of them, we've taken out 3 in short order![/quote]
Hopefully we'll add Riesel base 22 to that list soon, too! :smile:

mdettweiler 2009-10-08 22:01

Way cool! :w00t: :w00t: :w00t: :banana: :banana: :banana: It's very nice to see a base <=32 knocked out, that being this project's original scope and the range that's had the most work done. If I remember correctly, our last proof for bases <=32, Sierp. base 11, was more than a year and a half ago.

Now what would be really cool is if my quad turns up a prime on Sierp. base 33 within the next couple of days. :smile: Not quite <=32, but nonetheless it would be a great base to knock out.

Xentar 2009-10-10 17:50

Thank you all for the congratulations :smile:

Flatlander 2009-10-18 13:40

194*23^211140-1 (287518 digits) :smile:

Just leaves k=404 for R base 23.

Easily proven in my lifetime. [SPOILER][SIZE="1"](I'm changing my name to Methuselah.)[/SIZE][/SPOILER]

Siemelink 2009-10-18 20:22

[QUOTE=Flatlander;193164]
Easily proven in my lifetime. [SPOILER][SIZE="1"](I'm changing my name to Methuselah.)[/SIZE][/SPOILER][/QUOTE]

excellent!

Willem

gd_barnes 2009-10-19 05:25

[quote=Flatlander;193164]194*23^211140-1 (287518 digits) :smile:

Just leaves k=404 for R base 23.

Easily proven in my lifetime. [spoiler][SIZE=1](I'm changing my name to Methuselah.)[/SIZE][/spoiler][/quote]

Congrats on yet another large prime Chris! :smile::george:

m_f_h 2009-10-19 06:01

[QUOTE=Flatlander;193164]194*23^211140-1 (287518 digits) :smile:

Just leaves k=404 for R base 23.

Easily proven in my lifetime. [SPOILER][SIZE="1"](I'm changing my name to Methuselah.)[/SIZE][/SPOILER][/QUOTE]

Congrats on that nice prime.

For k=404, I'd suggest to look for exponents = 8 (mod 12)...


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