20210930, 20:04  #12 
Sep 2002
Database er0rr
2·7·281 Posts 
Recap:
Code:
{tst(n,a)=gcd(a^3a,n)==1&&kronecker(a^24,n)==1&&Mod(Mod(x,n),x^2a*x+1)^(n+1)==1;} {tst1(n,a,t)=gcd(t^21,n)==1&&gcd(a+t,n)==1&&gcd(a*t+1,n)==1&& Mod(t,n)^(n1)==1&&Mod(Mod(x+t,n),x^2a*x+1)^(n+1)==(a+t)*t+1;} {tst2(n,a,t,t2)=gcd(t^2t2^2,n)==1&&gcd((t*t2)^21,n)==1&& tst(n,a)&&tst1(n,a,t)&&tst1(n,a,t2);} It works for n prime, always (with kronecker(a^24,n)==1). I am firstly trying to construct a semiprime counterexample. Last fiddled with by paulunderwood on 20210930 at 20:08 
20211001, 11:32  #13  
Sep 2002
Database er0rr
3934_{10} Posts 
Quote:
1/A^q + t^q ==  (A + t)^q  / (A + t)^q mod p (I think). I can't make nor tails of it. Semiprime testing has reached p = 2521 and q = 2*k*(p1)+1 for k=4..14. It is slow going. [n, a, t, t2]=[79786523, 20692263, 4163322, 8326644] is a counterexample. Once again the primes win! Last fiddled with by paulunderwood on 20211001 at 13:27 

20211006, 15:57  #14 
Sep 2002
Database er0rr
3934_{10} Posts 
David Broadhurst gave me a file (attached to this message) of 100 small frauds that fool tst2, which took 42 seconds to produce.
He also found this 111 digit counterexample: Code:
{[n,a,t,t2]=[ 710641788142972835479085586911122643420643446726634578803992738008610099322008489919397662572833644270860844387, 481905506343238180263291435373078635219195334156921743957480549136989940684358483625484024629644986669892081256, 148287259869443430225832503946134162145762408831833753293682564445021118105658569785248629217653453554212689421, 238592749879783960713735924092293283842736794675381443476994761164913615939177038960039158690185545733634042511]; if(tst2(n,a,t,t2),print("\\\\ fooled at "#Str(n)" digits"));} \\ fooled at 111 digits 
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