20060807, 21:01  #34 
Apr 2004
273_{8} Posts 
distribution of Williams primes
I just checked b*(b+1)^n1 for b from 2 to 512, and n from 1 to 512.
Results are here: http://www.geocities.com/harvey563/wills.txt No prime values found for b = 37, 61, 82, 97, 112, 124, 127, 187, 226, 227, 232, 253, 267, 282, 292, 346, 356, 370, 382, 400, 415, 416, 442, 457, 477, 487, 493. I'm going to look at higher n values of these b. If anyone wants to share their results, post or email me them & I'll update the website. Harvey563 Last fiddled with by Harvey563 on 20060807 at 21:19 
20060807, 21:04  #35 
Jun 2003
3×5×107 Posts 
b=127 has been checked by RPS to 575K. So no need to waste time there.
Last fiddled with by Citrix on 20060807 at 21:10 
20060810, 07:25  #36  
Mar 2003
New Zealand
10010000101_{2} Posts 
Quote:
I implemented a filter that avoids sieving a sequence r*A^2+/B^2 with a prime p unless legendre(/+r,p)=1. The problem is that calculating the value of the Legendre symbol takes more time than is saved by not sieving the sequence, so I need to find a faster algorithm. However for r <= 6 I can use the form of the primes that have r as a quadratic residue from the table (see near the bottom of http://mathworld.wolfram.com/QuadraticResidue.html) and so don't need to compute Legendre. Does anyone know whether there is an algorithm for extending the table, or was it worked out by special case reasoning for each r <= 6? 

20060811, 23:18  #37 
Mar 2003
New Zealand
13·89 Posts 
I have finished sieving 4*5^n1 for 0 < n < 200,000 up to p=500e9. (Current status)
Version 0.4.2 of srsieve will recognise 4*5^n1 and only try factors p=1,9 (mod 10), so there is no need to use the patched version or to enter the mod=10,1,9 command line switch. It may also be faster for some of the other sequences like 2*3^n1, 5*6^n1, 6*7^n1 etc. if anyone is working on those. 
20060814, 21:15  #38  
Jun 2003
2^{2}·61 Posts 
Quote:


20060818, 23:16  #39  
Mar 2003
New Zealand
13·89 Posts 
Quote:
I have started PRP testing to n=90,000, any primes found beyond about n=100,000 should make the top 5000 list. 

20060922, 03:47  #40  
Mar 2003
New Zealand
13×89 Posts 
b*(b+1)^n1
Quote:
For 4*5^n1 sieving is up to 1e12 and PRP testing up to n=100,000. Sieve file is here. Now that the sieve is faster it is probably worthwhile sieving to at least 2e12 or further for PRP testing up to n=200,000. (This is quite a heavy sequence). 

20060922, 16:14  #41 
Jun 2005
3×11 Posts 
Now that sr5sieve has support for the quadratic residue stuff, perhaps we could do this and fill in the gaps (i.e. the sieve ranges where the other k's have been sieved, but 4 hasn't) later?

20060923, 01:17  #42 
Mar 2003
New Zealand
1157_{10} Posts 
Yes it would be more efficient. If others are interested enough (post now if you are) in PRP testing to higher levels we should do that, but personally I am happy to stop at n=200,000 and then go on to some of the other b*(b+1)^n1 sequences.

20060923, 10:12  #43 
Jun 2005
3×11 Posts 
I think I'd be interested in doing this. By how much does it reduce the performance of the sieve? Is anyone continuing sieving the 200K<n<2M range at the moment? (I can do this until it catches up with the other ks if needed.)
Last fiddled with by konrad127123 on 20060923 at 11:04 
20060926, 21:47  #44 
Mar 2003
New Zealand
1157_{10} Posts 
It shouldn't have a noticable effect on the sieve, but there may be a little extra work for the admins. I haven't done any sieving beyond what the files show.

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