20171231, 19:25  #122  
Nov 2008
2·3^{3}·43 Posts 
Quote:
When we say that a ≡ b (mod n), what we mean is that n divides ab exactly (or, equivalently, that a and b leave the same remainder on division by n). So, for example, 1 ≡ 11 (mod 5), because 5 divides 111 = 10 exactly. When n=5, indeed 2^n1 = 31 and (n+1)/2 = 3. These are not equal, but 2^n1 ≡ (n+1)/2 (mod n+2) is still true, because 7 divides 313 = 28 exactly, and 31 ≡ 3 (mod 7). The "%" operator gives the remainder you get when you divide one number by another. Note that if b = a%n, then a = kn+b for some integer k: that's what we mean by a remainder. Then ab = kn, so a ≡ b (mod n). This is how "mod" and "%" are related. For positive integers, a ≡ b (mod n) is equivalent to a%n = b%n. (You need to be careful with negative numbers because programming languages may define a%n to have the same sign as a.) Last fiddled with by 10metreh on 20171231 at 19:38 

20171231, 19:36  #123  
Aug 2006
5,923 Posts 
Quote:


20171231, 19:41  #124  
Feb 2017
A5_{16} Posts 
Quote:
No disagreement here: 31 mod 7 ≡ 3 However the logical == determinant means IS IDENTICAL. 31<>3 Consider the following: x==31 and x==31 mod 7....THEY ARE NOT THE SAME 

20171231, 19:45  #125 
Feb 2017
3·5·11 Posts 
Hi CRGreathouse
You seem to have no problem with gratis comments :) I know I am dumb, but please help me to understand and stop me from being a nuisance by posting the results for all to see and to analyse the outcomes. Ppl wil have a lot of faith in your results. 
20171231, 20:06  #126  
Aug 2006
5,923 Posts 
Quote:
I’ll be happy to carry out the analysis however you like, and write whatever supporting code is needed, as soon as the check clears in my bank account. Until then I recommend further study which will (in addition to enhancing your life) make it easier for you to understand the equivalence. If interested, forum members are usually more than happy to recommend resources. 

20171231, 20:35  #127  
Feb 2017
3·5·11 Posts 
Quote:
I respect that you have other tasks on the Site, it is just that I had thought that if you had done the analysis, that would have been much more authoritative. When I dream the first 100 million digit mersenne prime, I will hire your services :) Thanx for interactions and advice. 

20171231, 20:41  #128  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 
Quote:
Last fiddled with by science_man_88 on 20171231 at 20:47 

20171231, 22:25  #129 
"Curtis"
Feb 2005
Riverside, CA
10332_{8} Posts 

20171231, 22:39  #130 
Dec 2017
2·5^{2} Posts 
X!=Y means X does not equal Y.... right?
I read the title on a mathematical symbols keyboard. Wait, I am not replying to the right post, am I? If so, then just ignore this.
Last fiddled with by George M on 20171231 at 22:40 Reason: I wasn’t replying to the right post. 
20171231, 23:00  #131 
Feb 2017
3×5×11 Posts 
Hi George M
!= does mean "not equal to" in some computer code. 
20180101, 06:54  #132 
Feb 2017
3×5×11 Posts 
RETRACTION
Hi Everybody
I acknowledge that "my" algorithm is a "clone" of Fermat, after the answer to runs of the two algorithms by 10metreh, post #22, in the OMG, I cannot spam anymore in the forum Feedback where my question was answered!!!!!!!!!!111111 The results posted prove conclusively that "my" algorithm is a clone/copy of Fermat's. I apologise for not being to graps this earlier. Egg all over my face and many frustrated contributers. All I can do now is to provide the background work that I had used to derive "my" algorithm, if anybody might be interested. I did not use Fermat. Oh my gosh!!! 
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