Deployed some Pari code:
forprime(p=67,83,print(p);n=2^p1;for(a=2,999,for(b=0,a1,x=2^a+2^b;c=x;for(i=1,p2,c=(c^2*x)%n);c=(c^2)%n;if(c==1&&(ab)%p<>0,print("counterexample found: a="a", b="b)))))
[The forprimerange is to be set manually after every Mp=prime, e.g. next it would be forprime(p=97,103,...]
No counterexample for a<1000, b<a, p<71 yet.
I would guess there are likely to be counterexamples (e.g. Carmichael numbers with Hamming weight 2), but they're probably hard to find.
Last fiddled with by mart_r on 20110304 at 19:47
