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2019-04-17, 03:04   #9
dcheuk

Jan 2019
Pittsburgh, PA

233 Posts

Quote:
 Originally Posted by MathDoggy Counterexample to Lehmer's totient problem 2^521-1 is prime and when you put in the Phi function it is not equal to (2^521-1)-1 as Lehmer conjectured
I am confounded. We all know that $$p\in\text{prime}\implies\phi(p)=p-1$$, recall that the group of units for any prime number p has order (p-1).

How so that $$\phi\big(2^{521}-1\big)\neq(2^{521}-1)-1$$ but $$2^{521}-1$$ is a prime?