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 gd_barnes 2009-10-19 06:53

[quote=m_f_h;193220]Congrats on that nice prime.

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

Can you show how you came up with that? While many of the exponents that would need to be searched will be n == 8 mod 12, it would not be a good idea to look at ONLY n == 8 mod 12. Some n == 4 mod 12 must also be searched.

Proof:

The factors of 3, 5, and 13 leave n == 4, 8 mod 12 remaining.

17 is a factor of n == 4 mod 16.

That leaves n == 8, 16, 28, 32, 40, 44 mod 48 remaining.

To bring it down to n == 8 mod 12 would require that n == 16, 28, and 40 mod 48 all be eliminated by a specific covering set of factors. (Would leave n == 8, 32, and 44 mod 48, which are all n == 8 mod 12.) The first 3 occurrences of each of the n==16,28,40mod48 n-values, i.e. n=16, 28, 40, 64, 76, 88, 112, 124, & 136 have smallest factors of 43, 19, 31, 19, 862607762761, 97, 2607312184177832981, 607, & 19 respectively.

The two huge smallest factors for n=76 and n=112 clearly demonstrate there is no covering set of factors for n == 16, 28, and 40 mod 48. Since these are all n == 4 mod 12, we can conclude:

Some but not all n == 4 or 8 mod 12 must be searched and it can be narrowed down to 1/8th of all n-values (6 out of every 48) with the above. It could also be narrowed further by eliminating the factor of 19 that occurs every n == 1 mod 9 and the factor of 31 that occurs every n == 0 mod 10. But showing them here would be cumbersome as it would require that we go to n == xxx mod 720.

Besides, srsieve and sr1sieve will quickly eliminate the appropriate n-values. There is already posted a file on the web page.

Edit: If anyone is interested in seeing the factorizations of the first 150 n-values for 404*23^n-1, check out Syd's factoring database [URL="http://factorization.ath.cx/search.php?query=404*23%5En-1&v=n&n=1&EC=1&E=1&Prp=1&P=1&C=1&FF=1&CF=1&of=H&pp=150"]here[/URL]. I was quickly able to fully factor the first 50 n-values. For n-values > 50, the database quickly automatically factors to 10e5. Some of those are fully factored and some aren't. I ran some ECM curves on the n-values that pertained to this (as well as a few others) and came up with the large factors shown above and others that are > 10e5.

Gary

 MyDogBuster 2009-10-21 17:39

Sierp Base 23

Okay guys and girls - a true monster

68*23^365239+1 is prime [URL]http://primes.utm.edu/primes/page.php?id=90552[/URL]

This proves the conjecture, Doc Caldwell likes it.

497358 digits. This is my largest prime yet by about 200K digits. It hits the big time at 94th place in the Top 5000.

Releasing the base.

 Flatlander 2009-10-21 18:17

Somebody catch Gary!

Congratulations Ian :groupwave::bow wave:

 Xentar 2009-10-21 19:26

Congratulations - another one proven :groupwave:

[QUOTE=MyDogBuster;193471]Okay guys and girls - a true monster

68*23^365239+1 is prime [URL]http://primes.utm.edu/primes/page.php?id=90552[/URL]

This proves the conjecture, Doc Caldwell likes it.

497358 digits. This is my largest prime yet by about 200K digits. It hits the big time at 94th place in the Top 5000.

Releasing the base.[/QUOTE]

Excellent stuff!

Willem.

 gd_barnes 2009-10-22 01:33

[quote=MyDogBuster;193471]Okay guys and girls - a true monster

68*23^365239+1 is prime [URL]http://primes.utm.edu/primes/page.php?id=90552[/URL]

This proves the conjecture, Doc Caldwell likes it.

497358 digits. This is my largest prime yet by about 200K digits. It hits the big time at 94th place in the Top 5000.

Releasing the base.[/quote]

Oh yeah!! Here we go again! A score of 50 for this truly huge monster!!

We've now proven Sierp bases 18, 23, 57, and 99 in the last month or so and nearly 18 months after proving our first big one...Sierp base 11. There were so many Sierp bases with only 1 k remaining, it had to start happening at some time. I think it's time to prove a Riesel base now.

A huge congrats Ian!

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

I have to razz you here...So, you're releasing the base, eh? Just what would someone else test on it...a larger k=68 prime? lmao

Gary

 gd_barnes 2009-10-22 01:48

[quote=MyDogBuster;193471]Okay guys and girls - a true monster

68*23^365239+1 is prime [URL]http://primes.utm.edu/primes/page.php?id=90552[/URL]

This proves the conjecture, Doc Caldwell likes it.

497358 digits. This is my largest prime yet by about 200K digits. It hits the big time at 94th place in the Top 5000.

Releasing the base.[/quote]

One more bit of interesting info. about this one: As far as I can tell, this is the 1st base proven with TWO primes of n>100K! :smile:

 MyDogBuster 2009-10-22 01:53

[QUOTE]I have to razz you here...So, you're releasing the base, eh? Just what would someone else test on it...a larger k=68 prime? [/QUOTE]

After getting ripped for NOT releasing bases, I'm just covering my butt.:crank:

Thanks all.

 mdettweiler 2009-10-23 05:22

[quote=MyDogBuster;193471]Okay guys and girls - a true monster

68*23^365239+1 is prime [URL]http://primes.utm.edu/primes/page.php?id=90552[/URL]

This proves the conjecture, Doc Caldwell likes it.

497358 digits. This is my largest prime yet by about 200K digits. It hits the big time at 94th place in the Top 5000.

Releasing the base.[/quote]
I believe I've already stated this in another thread, but congratulations again for proving this base, and with such a humongous prime to boot! It's very nice to see another of the bases <32 proven, one of my personal goals that I've had for a long time.

Interestingly enough, as I believed had been mentioned a bit in some other threads, I had originally been hoping to reserve this base and run it during my trip before you'd nabbed it. But, now that I think about it, since my quad ended up being off all throughout my trip, if I had reserved it, it probably would be hovering only around 302K or so right now and a few weeks away from the proof! :smile: So, indeed, it definitely worked out quite nicely that you did it. Hey, whatever works--doesn't matter who does it as long as it gets done as quickly as possible. :tu:

I see now that you've also grabbed Sierp. base 12, another base I was considering doing in the future. I hope that one goes well for you too--I did quite a bit of searching on it in the past and it definitely seems overdue for a prime, which would, like your base 23 prime, be extremely large. Now that Riesel base 23 has been whittled down to one k by Chris, I'll probably tackle it if it's still at large when I'm done with my current work.

Meanwhile, I've got a base 206 prime coming up soon that I'll prove in a moment. I must admit I really have no idea what size it is since I'm not very familiar with base 206, but I'll be sure to calculate it when I report it here. :smile:

 Flatlander 2009-11-06 20:07

117690*31^108349-1 is prime.

 gd_barnes 2009-11-06 20:45

[quote=Flatlander;195071]117690*31^108349-1 is prime.[/quote]

Nice one Chris. Our 3rd top-5000 base 31 prime. This is becoming old hat for you. :smile:

Riesel base 31 could be called "8-or-bust #2". :smile: With 8 k's remaining at n=100K, it now has 7 remaining.

As heavy-weight as it is, this might be a fun one to make a team effort out of at some point.

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