most recent 30 from http://mathoverflow.net 2013-05-21T07:42:36Z http://mathoverflow.net/feeds/question/79844 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/79844/how-to-prove-prime-numbers GarouDan 2011-11-02T15:42:27Z 2011-11-02T15:42:27Z

<blockquote> <p>$f(0)=4$</p> <p>$f(x+1)=f(x)^2-2$</p> <p>$\text{if} \quad 2^{x+2}-1|f(x) \quad \text{then} \quad 2^{x+2}-1 \quad \text{is prime}$</p> </blockquote> <p>How to prove that?</p> <p>Example:</p> <p>$x=1$</p> <p>$f(1)=14$, </p> <p>$2^{1+2}-1=7$</p> <p>and </p> <p>$7|f(1) \implies 7$ is prime.</p>