20060716, 02:22  #1 
Mar 2003
New Zealand
13·89 Posts 
Williams' sequence 4*5^n1 (A046865)
The sequence A046865 is mentioned in secion A3 of R. K. Guy's "Unsolved Problems in Number Theory".
The terms of the sequence are the primes of the form 4*5^n1, a specific case of Williams' sequences of primes of the form (r1)*r^n1. I will start sieving with srsieve. If anyone else is interested in extending this sequence, perhaps we could add it to the Base 5 Sierpinski/Riesel distributed sieve when I catch up (say when sieving reaches p=200e9)? The sequences in other bases, A003307, A079906, A046866, etc. could also be extended, but would have to be sieved individually. 
20060716, 16:45  #2 
Jun 2003
3×23^{2} Posts 
I am interested in helping out. But what is the open problem related to these numbers? what is the weight of these numbers?
Have you tried to search (b1)*b^n+1? For fixed n and variable b. Can b1 ever be a sierpinki or riesel number for base b? I am more interested in working on the two questions stated above, if there is no open problems related to these numbers. Last fiddled with by Citrix on 20060716 at 16:46 
20060717, 01:24  #3  
Mar 2003
New Zealand
13·89 Posts 
Warning: this sequence tickles a bug present in srsieve versions 0.3.0 to 0.3.6, upgrade to 0.3.7 or later.
Quote:
If n > 0 and n=2m then 4*5^n1 = (2*5^m1)(2*5^m+1), so only the odd terms have to be sieved. Also all the factors for the odd terms appear to end in either 1 or 9, so the sieve speed can be doubled by filtering out those ending in 3 or 7. Quote:
I only sieved 4*5^n1 with 0 < n <= 2e6 (the distributed sieve range) up to p=6e9, I will stop there, but will continue sieving a smaller range, say 0 < n <= 200,000 since that should be enough to find a few more terms to extend the sequence. If anyone is interested in sieving 5*4^n1 I have posted the current sieve in NewPGen format and a modified version of srsieve which only sieves primes that are 1 or 9 mod 10 here. 

20060717, 13:58  #4 
Jun 2003
2^{2}·61 Posts 
i can sieve these for a while. what program would be best(fastest) to test these numbers for primality?

20060717, 14:30  #5  
Jun 2003
3×23^{2} Posts 
Quote:
Thankyou. 

20060717, 15:20  #6  
Aug 2005
Brazil
2×181 Posts 
Quote:


20060717, 15:46  #7 
Jun 2003
2^{2}·61 Posts 
Sequence has been extended
Enter expression followed by carriage return:
4*5^15393+1 Primality testing 4*5^15393+1 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 2 Running N1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Running N+1 test using discriminant 7, base 3+sqrt(7) Calling N+1 BLS with factored part 100.00% and helper 0.11% (300.12% proof) 4*5^15393+1 is prime! (215.8260s+0.0009s) Is there someone I can report this to? Last fiddled with by antiroach on 20060717 at 15:46 
20060717, 23:31  #8 
Jun 2003
2^{2}·61 Posts 
Status Update
I sieved the 0<=n<=2M file upto 12e9. Here's the srsieve formatted file: http://s89744942.onlinehome.us/results.zip
I also started factoring the numbers. Im upto like n = 30k. I plan on going upto like n=50k and then im going to switch over to working on the 6*7^n1 sequence. 
20060718, 03:10  #9  
Mar 2003
New Zealand
485_{16} Posts 
Quote:


20060719, 14:08  #10 
Jun 2003
2^{2}·61 Posts 
I prp'd 4*5^n1 upto n = 50000 without finding any more primes.

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