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2009-10-19, 06:53
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#89 | |
May 2007
Kansas; USA
101·103 Posts |
Quote:
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 here. 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 Last fiddled with by gd_barnes on 2009-10-19 at 07:31 Reason: edit |
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2009-10-21, 17:39
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#90 |
May 2008
Wilmington, DE
22×23×31 Posts |
Sierp Base 23
Okay guys and girls - a true monster
68*23^365239+1 is prime http://primes.utm.edu/primes/page.php?id=90552 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. |
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2009-10-21, 18:17
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#91 |
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I quite division it
"Chris"
Feb 2005
England
1000000111012 Posts |
Somebody catch Gary!
Congratulations Ian  
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2009-10-21, 19:26
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#92 |
Sep 2006
11×17 Posts |
Congratulations - another one proven
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2009-10-21, 19:33
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#93 | |
Jan 2006
Hungary
10C16 Posts |
Quote:
Willem. |
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2009-10-22, 01:33
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#94 | |
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May 2007
Kansas; USA
101·103 Posts |
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!  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 Last fiddled with by gd_barnes on 2009-10-22 at 01:34 |
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2009-10-22, 01:48
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#95 | |
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May 2007
Kansas; USA
101·103 Posts |
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2009-10-22, 01:53
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#96 | |
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May 2008
Wilmington, DE
22×23×31 Posts |
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 Thanks all. |
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2009-10-23, 05:22
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#97 | |
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A Sunny Moo
Aug 2007
USA (GMT-5)
624910 Posts |
Quote:
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! 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.  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.
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2009-11-06, 20:07
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#98 |
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I quite division it
"Chris"
Feb 2005
England
207710 Posts |
117690*31^108349-1 is prime.
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2009-11-06, 20:45
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#99 | |
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May 2007
Kansas; USA
101×103 Posts |
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Riesel base 31 could be called "8-or-bust #2". 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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