Friday, December 19, 2003

Desperately Seeking Primes

So it's going to be 100 K$ for the first 10 million digit prime as stated in this EFF Release. An interesting approach is by these guys, but I am wondering if one should not be looking into a totally different approach. Say for instance use the connection between the heat equation and the Euler product . Another interesting approach could be found here.. One of the most interesting graphs i have seen on this subject is the animation for the prime counting function as shown in here. Maybe if one were to use a wavelet decomposition of this function so we could clearly detect the jumps of that function for any large numbers (since we seem to know Riemann's zero up to 10^22)? what would initially be interesting is to study how many zeros of the Riemann's function do you need to know to obtain a good resolution on the \psi_0 function ? So now the question is really can we find Riemann's zeros around 10^(10^6) ? The latest prime found has 6 millions digits. The race is on.

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