20200124, 06:49  #12 
Romulan Interpreter
Jun 2011
Thailand
13×733 Posts 

20200124, 07:01  #13  
Romulan Interpreter
Jun 2011
Thailand
2539_{16} Posts 
Quote:
log(a*b)=log(a)+log(b) log(a^b)=b*log(a) log_{b}(x)=log_{c}(x)/log_{c}(b) (change of base) In your case, log_{10}(231*2^2335281)=log_{10}(231)+2335281*log_{10}(2)~=2.3+2335281*0.3 = 2.3+702,989.6 Your confusion may be because log in your case is assumed to be any base (like natural log). If you take base 10, log_{10}(10) is 1, so the last part is gone. Note that in windows calculator, log is base 10 (what we use in school to write like lg) and not base e (what we used in school to write like ln). Last fiddled with by LaurV on 20200124 at 07:02 

20200124, 13:47  #15  
Feb 2017
Nowhere
11E7_{16} Posts 
Quote:
log(N+1) = log(10) + 13509*log(2), so we have 1 + floor(log(N+1)/log(10)) = 2 + floor(13509*log(2)/log(10)), which is 4068. Siccing the mighty PariGP on the previous query, Code:
? 1+floor((log(231) + 233528*log(2))/log(10)) %2 = 70302 Also, I meant floor(), the integer floor. The integer ceiling of an exact integer is that integer, so it gives the wrong answer for exact powers of ten; ceil(log(100)/log(10)) is 2, not 3. 

20200124, 14:50  #16  
Random Account
Aug 2009
1,949 Posts 
Quote:
Quote:
Quote:
I looked at some of the prime results posted above. I noticed some of them use composite numbers, like 231*2^23352811. At first, I thought this would be selfdefeating, but then, I remembered some basics: Odd number * odd number is an odd number. Just in case, I steered around this. Below is a PFGW ABC2 I had been experimenting with. Code:
ABC2 $a*2^$b1 a: primes from 100 to 500 b: from 4256191 to 4256191 I want to thank all of you for your feedback so far. Most kind. Last fiddled with by storm5510 on 20200124 at 14:51 Reason: Typo 

20200124, 17:27  #17 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
2×2,473 Posts 
This interesting discussion should be moved to another thread.

20200125, 11:55  #18 
Random Account
Aug 2009
11110011101_{2} Posts 

20200126, 15:06  #19 
Random Account
Aug 2009
1,949 Posts 
I have been looking at these pages for several days and all the results I see are in the form of x*2^{p}1. Yes, this is an expansion of the standard Mersenne format. Why not be more creative? Dr. NIcely's web site is a good example. I have tested other combinations with PFGW and they all run fine. Naturally, if the goal here is to keep everything in the Mersenne purview, then I understand. Just writing outloud...

20200126, 18:13  #20 
"Curtis"
Feb 2005
Riverside, CA
12DE_{16} Posts 
This project specifically is to search for k * 2^n1. So, it should not surprise you that all these primes are of that form. Anyone could surely broaden their search to other forms, and there are many other projects to tackle those other types; this one only tests and coordinates this one form.
We use LLR to test for primality, as it is much faster than PFGW for these forms. 
20200126, 20:10  #21  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
22367_{8} Posts 
Quote:
So don't use 'p' notation, and then you just fall through into the Riesel primes. Congrats for rediscovering them! 

20200127, 01:18  #22 
Random Account
Aug 2009
1,949 Posts 
After some thought, I think I can explain what I was getting at. Consider the following:
Code:
2^501 = 1,125,899,906,842,623 2^511 = 2,251,799,813,685,247 Code:
? * (2^19518711)  (2^366497) If my thinking seems sort of loony, please forgive me. I have had the flu for a week and, at times, the fever which goes with it. 
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