mersenneforum.org Riesel base 16 - team drive #2
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 2013-11-24, 18:48 #199 KEP Quasi Admin Thing     May 2005 22·241 Posts R16 is at n=360K, nothing found, continuing happily
 2013-11-29, 18:43 #200 KEP Quasi Admin Thing     May 2005 22·241 Posts 7673*16^366247-1 is prime, unfortunantly it doesn't seem to prime k=7673 for b=256. If anyone can tell me how this prime can also make 7673*256^n-1 prime, I'm more than happy to know. It appears that there could be a little to premature assumption that once b=16 primes k=7673 it also automatically primes k=7673 for b=256, wich would be correct if n was even, since the transformation requires a division of n by 2, in order for a b=16 number to be able to transform into a b=256 number. If there is something I'm missing, please enlighten me, but it could as far as I'm concerned be that a condition has to be added, like forinstance n having to be equal and not odd or however it would be translated Overall, does this mean, that k's we thought were searched by SOB, PSP and TRP in fact really hasn't been completely checked to that n-value? Does this mean that k's that has been assumed primed by a lower base prime in fact isn't primed when all comes to all? Anyway at least 1 k less so only 199 k's remain for the base=2 and powers of base=2 conjectures
 2013-11-29, 19:16 #201 Siemelink     Jan 2006 Hungary 22·67 Posts [QUOTE=KEP;360645]7673*16^366247-1 is prime, unfortunantly it doesn't seem to prime k=7673 for b=256. I like that 7673 is prime too. Too bad 366247 isn't. Willem.
2013-11-29, 19:20   #202
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

10000101010112 Posts

Quote:
 Originally Posted by KEP 7673*16^366247-1 is prime, unfortunantly it doesn't seem to prime k=7673 for b=256. If anyone can tell me how this prime can also make 7673*256^n-1 prime, I'm more than happy to know. It appears that there could be a little to premature assumption that once b=16 primes k=7673 it also automatically primes k=7673 for b=256, wich would be correct if n was even, since the transformation requires a division of n by 2, in order for a b=16 number to be able to transform into a b=256 number. If there is something I'm missing, please enlighten me, but it could as far as I'm concerned be that a condition has to be added, like forinstance n having to be equal and not odd or however it would be translated Overall, does this mean, that k's we thought were searched by SOB, PSP and TRP in fact really hasn't been completely checked to that n-value? Does this mean that k's that has been assumed primed by a lower base prime in fact isn't primed when all comes to all? Anyway at least 1 k less so only 199 k's remain for the base=2 and powers of base=2 conjectures
First, some facts...
256/16 = 2^4
16^(4n) = 256^n
k*16^(4n)-1 = k*256^n-1

What this means:
If the n in base 16 is divisible by 4, then it also makes a prime in base 256. Since I can see that this n is odd, it does not make a prime in any base above 16.

Last fiddled with by Mini-Geek on 2013-11-29 at 19:23

2013-11-29, 20:30   #203
KEP

May 2005

22·241 Posts

Quote:
 Originally Posted by Mini-Geek First, some facts... 256/16 = 2^4 16^(4n) = 256^n k*16^(4n)-1 = k*256^n-1 What this means: If the n in base 16 is divisible by 4, then it also makes a prime in base 256. Since I can see that this n is odd, it does not make a prime in any base above 16.
Okay, I thought a bit about what you wrote and everything is a bit more clear now, it's obvious that all even n is covering n/2 for base 256 when they are tested in base 16 so when I get to n=500K, all k's remaining should have been tested to n=250K for b=256. However, due to stop on prime function, I'm no longer testing k=7673, so the testdepth on b=256 should reflect that I only tested k=7673 to n-1 div 2

Sorry for any inconvenience, I guess I confused myself a little

2013-11-29, 20:45   #204
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17×251 Posts

Quote:
 Originally Posted by KEP Sorry for any inconvenience, I guess I confused myself a little
I think I did that too. 16^(4n) = 256^n is not true, this is (thanks Wikipedia):

16^(2n) =
(16^2)^n =
256^n

Part of my conclusion was still correct though: the fact that n is odd means that it's not a base 256 prime.

Last fiddled with by Mini-Geek on 2013-11-29 at 20:49

 2013-11-30, 00:07 #205 gd_barnes     May 2007 Kansas; USA 72×211 Posts Nice prime Kenneth. It's too bad that n was not even to make a R256 prime. I have now reflected R256 k=7673 at n=183K, close enough to the depth that you reached base 256. I also have removed it as reserved by this drive. Effectively it's just lumped in with "other k's" now. Last fiddled with by gd_barnes on 2013-11-30 at 00:22
2013-11-30, 20:49   #206
KEP

May 2005

3C416 Posts

Quote:
 Originally Posted by gd_barnes Nice prime Kenneth. It's too bad that n was not even to make a R256 prime. I have now reflected R256 k=7673 at n=183K, close enough to the depth that you reached base 256. I also have removed it as reserved by this drive. Effectively it's just lumped in with "other k's" now.
Thanks. It was really bad, that it did not effectively make a b=256 prime, however if anyone is up for it, they can test to n=250K using the presieved file for this drive, testing only even n

Who knows, maybe I'll be able to find a Top1000 prime next time

 2013-12-16, 15:21 #207 KEP Quasi Admin Thing     May 2005 22·241 Posts I missed an update due to private real life commitments but... R16 is at n=400K, nothing new found, continuing happily
 2013-12-29, 14:40 #208 KEP Quasi Admin Thing     May 2005 22×241 Posts R16 is at n=420K. Nothing new found. Continuing happily. If no further primes is found I expect the entire base to be at n=>500K around 19th of february 2014 Next status will be around January 11th, since it appears to take approximately 13 days to climb 20K n's... Regards Kenneth
 2014-01-09, 17:40 #209 KEP Quasi Admin Thing     May 2005 22×241 Posts Another prime found k=3620 eliminates 2 unprimed k's, since 3620*16^435506-1 also transforms into 3620*256^217753-1 So this time I was lucky and eliminated 2 k's in stead of 1 k. On a sidenote, this is my first prime to enter the "Short list" Status is currently all remaining 12 k's is tested to n=435000 Kenneth

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