20130708, 23:46  #12 
Jun 2003
62E_{16} Posts 
Looking more into this: Find bases such that base+1 and base1 are not smooth. Otherwise you easily get trivial factors.
Related question: For each base find the lowest starting term that results in trivial factors. What is the lowest one for 2? 
20130709, 01:14  #13 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 
Code:
for(k=1,100000000000000,for(n=1,1000000000,if(isprime(k*2^n+1),print1(n",");k=k*2^n;break()))) Last fiddled with by science_man_88 on 20130709 at 01:19 
20130709, 09:47  #14 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
5922_{10} Posts 
With PFGW I don't really think it is worth bothering with that sort of thing. Almost all the time is spent trial factoring the candidates with large factors and prp testing them. Calculating the candidates is trivial.

20130709, 14:21  #15 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2·3^{2}·7·47 Posts 
Base 12 with prime b+1, b1 ends in a trivial factor for k=1 c=+1
http://factordb.com/index.php?query=...at=1&sent=Show Base 2 gets off lighter because it doesn't matter if every term is divisible by b1=1. b=12, k=1, c=1 hasn't terminated yet for me. 
20130709, 15:36  #16  
Jun 2003
2·7·113 Posts 
Quote:
FYI: I tested b=2, k=1, c=1 further upto 65,000 bits... no primes. This is how I did it with the (f Flag) Code:
ABC2 ((((((((((((((((1*2^1+1)*2^1+1)*2^2+1)*2^1+1)*2^5+1)*2^1+1)*2^1+1)*2^29+1)*2^3+1)*2^37+1)*2^31+1)*2^227+1)*2^835+1)*2^115+1)*2^7615+1)*2^6071+1)*2^$a+1 a: from 1 to 50000 Last fiddled with by Citrix on 20130709 at 15:37 

20130731, 01:51  #17  
Jun 2003
11000101110_{2} Posts 
Quote:


20130815, 22:15  #18 
Jun 2003
11000101110_{2} Posts 
Code:
((((((((((((((((1*2^1+1)*2^1+1)*2^2+1)*2^1+1)*2^5+1)*2^1+1)*2^1+1)*2^29+1)*2^3+1)*2^37+1)*2^31+1)*2^227+1)*2^835+1)*2^115+1)*2^7615+1)*2^6071+1)*2^218431+1 is prime! The nash weight of this new number is even lower. Last fiddled with by Citrix on 20130815 at 22:16 
20130824, 05:24  #19 
Jun 2003
11000101110_{2} Posts 
Complete to 100K. continuing.
I have written a sieve for these numbers... so things are easier now. Could one of the moderators move this thread to the open projects section. Thx 
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