--- Mark Underwood <

mark.underwood@...> wrote:

> And to top it all off:

>

> x^8 - x^4 + 1 has no prime factors below 73 (!)

Now do you see why PIES has such the incredible density of primes that it has?

The above is just Phi(24). PIES is looking at Phi(49152) and Phi(98304). The

super-fruit subprojects can have even higher densities.

One puzzle I set the PIES guys was the following:

<<<

Mathematicians are invited to calculate the relative density of primes

of the form Phi(24576,715*b^2) compared to arbitrary numbers of the

same size.

>>>

Just finding out what its smallest possible factor is should be an eye-opener.

Phil

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