--- On Tue, 8/31/10, Sebastian Martin Ruiz <

s_m_ruiz@...> wrote:

> Hello all:

>

> I have obtained an equivalence for prime numbres:

>

> p is prime

>

> if and only if

>

> Sum {for z=1 to p^(1/2)} Floor[(z*Floor[(p+z)/z]/(p+z)] = 1

>

> and better:

>

> Sum {for z=1 to p} Floor[(z*Floor[(p+z)/z]/(p+z)] =d(p) the

> number of divisors of p.

I'm sure you've obtained these about a dozen times in the last few years, as it's just a trivial obfuscation of

Sum[z=a..b] { 1 if z|p; 0 otherwise } = # divisors of z in [a..b]

z*Floor((p+z)/z) is clearly just (p+z)-((p+z)%z)

So Floor(z*Floor((p+z)/z)/(p+z)) is clearly only 1 when (p+z)%z==0, i.e. when z|p, and otherwise 0.

Your use of (p+z)%z rather than p%z is purely obfuscation in order to make it appear that you've come up with a new expression, but all you've done is make something no more useful, but even uglier than previous ones.

Phil

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