20120402, 05:20  #1 
Nov 2011
2^{2}·3 Posts 
Proof of Primality Test for Fermat Numbers
Let be a Fermat number of the form :
Next , let's define sequence as : Then : Proof is attached . Any constructive comment is appreciated . 
20120402, 06:01  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9,901 Posts 
Not too late for the April 1st! (at least in our TZ)

20120402, 07:24  #4 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
Nice link.
Going by the bottom comment on the only answer, the two tests are exactly the same, and the other test is from 1960, so... I guess you could see if your proof improves the original proof? (I don't have anywhere near the sort of knowledge to examine the proofs.) 
20120402, 07:40  #5  
Nov 2011
2^{2}×3 Posts 
Quote:


20120402, 08:02  #6 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
16065_{8} Posts 
No, I'm pretty sure they're the same. R0=S0=8; Rn=R(n1)^22; Sn=(S(n1)^22)^22. Therefore, S1=R2, and trivially R2n=Sn for all n (n>=0). Your test ends with i=2^(n1)1, while the other test ends with k=2^n2=2i, so the sequences are identical. All your sequence does is the same as two iterationsof R, and then do half the iterations, but that's still exactly the same thing.
Last fiddled with by Dubslow on 20120402 at 08:05 
20120402, 08:59  #7 
Mar 2010
192_{10} Posts 
Sorry i did not notice the assumption n>=2
Last fiddled with by literka on 20120402 at 09:05 
20120402, 09:03  #8 
Nov 2011
2^{2}·3 Posts 
Yes , you have missed condition :

20120402, 09:13  #9 
"Tapio Rajala"
Feb 2010
Finland
3^{2}·5·7 Posts 
As underlined by Dubslow, the most satisfactory answer one can give is already given in Emil Jeřábek's comment (behind the link I posted). The test is the same as Inkeri's. So, nothing new.

20120402, 11:40  #10 
Mar 2010
192_{10} Posts 
I noticed this shortly after uploading post. I cannot compare your work with work of Inkeri, which I do not know. I have few editorial remarks, which may be useful for you. Everywhere you use sign of equivalence but in Lemma 2.1. you use sign of equality. I would, in your place, specify the range of x, y, in Lemma 2.1., since you use Lemma 2.1. for noninteger elements. 
20120402, 12:31  #11  
Nov 2011
2^{2}×3 Posts 
Quote:


Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Prime numbers test primality  with proof written in invisible ink  Godzilla  Miscellaneous Math  40  20181017 00:11 
The fastest primality test for Fermat numbers.  Arkadiusz  Math  6  20110405 19:39 
PRIMALITY PROOF for Wagstaff numbers!  AntonVrba  Math  96  20090225 10:37 
A primality test for Fermat numbers faster than Pépin's test ?  T.Rex  Math  0  20041026 21:37 
Two Primality tests for Fermat numbers  T.Rex  Math  2  20040911 07:26 