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Old 2011-03-04, 19:42   #18
mart_r
 
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Dec 2008
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Deployed some Pari code:
forprime(p=67,83,print(p);n=2^p-1;for(a=2,999,for(b=0,a-1,x=2^a+2^b;c=x;for(i=1,p-2,c=(c^2*x)%n);c=(c^2)%n;if(c==1&&(a-b)%p<>0,print("counterexample found: a="a", b="b)))))
[The forprime-range 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 2011-03-04 at 19:47
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