20110718, 21:36  #1 
Jul 2011
1110101_{2} Posts 
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. 
20110719, 02:21  #2 
Apr 2010
Over the rainbow
2·1,303 Posts 
http://factordb.com/index.php?query=%2811235813*%282^98%291%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 20110719 at 02:26 
20110719, 13:03  #3 
Jul 2011
3^{2}·13 Posts 
Values for n that generate primes for k*2^n1 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 20110719 at 13:10 
20110719, 20:10  #4 
Jul 2011
3^{2}×13 Posts 
Found n = 161927 for the above prime series.

20110720, 04:46  #5 
Nov 2003
2·1,811 Posts 
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.

20110720, 11:59  #6  
Jul 2011
1110101_{2} Posts 
Quote:
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. 

20110720, 12:38  #7  
Mar 2006
Germany
2^{2}×727 Posts 
Quote:
See also here for some information, how the Nash weight is defined. 

20110720, 13:03  #8  
Jul 2011
3^{2}·13 Posts 
Quote:
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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