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Old 2011-07-18, 21:36   #1
SaneMur
 
Jul 2011

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Default Reserving k = 11235813

Please tell me nobody is working on this constant!

(k*(b^n)) - 1 = 3560771273375535719079719333026332671 and is prime for k = 11235813, b = 2, and n = 98.
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Old 2011-07-19, 02:21   #2
firejuggler
 
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http://factordb.com/index.php?query=%2811235813*%282^98%29-1%29


it is indeed prime.
it is very easy to prove number that short to be prime or not.
unless you are looking in the 300 digits, it is fairly easy to determine (read almost instant) if a number is a probable prime or a composite

Last fiddled with by firejuggler on 2011-07-19 at 02:26
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Old 2011-07-19, 13:03   #3
SaneMur
 
Jul 2011

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Values for n that generate primes for k*2^n-1 with k = 11235813:

2, 23, 26, 28, 80, 83, 98, 127, 152, 182, 347, 388, 392, 400, 416, 542, 830, 839, 1292, 1436, 2572, 4280, 9724, 13843, 15992, 17084, 34076, 44483, 45692, 52036, 85864, 97640, 113716

Still searching.

Last fiddled with by SaneMur on 2011-07-19 at 13:10
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Old 2011-07-19, 20:10   #4
SaneMur
 
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Found n = 161927 for the above prime series.
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Old 2011-07-20, 04:46   #5
Kosmaj
 
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Nice primes! But to qualify for the list of 5000 largest primes maintained at primes.utm.edu the binary exponent has to be about n=666,700 or larger. You can keep on testing all exponents in order until you reach that level but that's going to take quite a while. Another approach is to switch a few clients to test n>666700 now, so that you can report your first prime sooner. You can fill the gap later.
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Old 2011-07-20, 11:59   #6
SaneMur
 
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Quote:
Originally Posted by Kosmaj View Post
Nice primes! But to qualify for the list of 5000 largest primes maintained at primes.utm.edu the binary exponent has to be about n=666,700 or larger. You can keep on testing all exponents in order until you reach that level but that's going to take quite a while. Another approach is to switch a few clients to test n>666700 now, so that you can report your first prime sooner. You can fill the gap later.
Thanks. I was just looking at the top 5000 list and saw what it takes for powers of 2 to get near there.

I didn't sieve too deeply for n< 250K but I have been sieving n > 250K since I started a few days ago. I plan on using 2 CPUs for n > 250K when the time arrives.

By the way, are there any good sites/PDFs on how to compute the Nash Weight for a given constant? I see mine is 1990 for 11235813 and I'd like to know more about this. Google finds all kind of "weight loss" stuff, or Nash's celebrated paper on competitive dynamics, which is not what I am looking for.
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Old 2011-07-20, 12:38   #7
kar_bon
 
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Quote:
Originally Posted by SaneMur View Post
By the way, are there any good sites/PDFs on how to compute the Nash Weight for a given constant? I see mine is 1990 for 11235813 and I'd like to know more about this. Google finds all kind of "weight loss" stuff, or Nash's celebrated paper on competitive dynamics, which is not what I am looking for.
See this thread for tools to calculate the Nash weight for k*2^n-1.

See also here for some information, how the Nash weight is defined.
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Old 2011-07-20, 13:03   #8
SaneMur
 
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Quote:
Originally Posted by kar_bon View Post
See this thread for tools to calculate the Nash weight for k*2^n-1.

See also here for some information, how the Nash weight is defined.
Thanks Karsten! And thanks for adding my data to the Riesel pages. Right now I am at n = 194476 and still searching (no new primes since yesterday).

My effective exponent search rate (eesr) is about 1 n per second now (it takes about 30 seconds for each exponent @ ~200K, and the sieving is such that 30 exponents are "skipped" on average) but this will slow down soon enough.
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