My mistake here was that:

PrimePi[n]/CompositePi[n]=(1/Log[n])/(1-1/Log[n])=1/(Log[n]-1)

That checks to

give:

PrimePi[n]=n/Log[n]

I had the ratio not the density.

I'm sorry.

Roger Bagula wrote:

> 1) Limit[Prime[n], n--> Infinity]=n*Log[n] ( Euler, I think)

> 2) Limit[PrimePi[n],n->Infinity]=n/Log[n] (Hadamard)

> 3) Limit[PrimePi[n]/CompositePi[n],n-> Infinity]=1/Log[n] ( from

> Ulam, in both books I have by him)

>

> How 3) can be made to contradict 2):

> PrimePi[n]+CompositePi[n]=n

> PrimePi[n]/CompositePi[n]=PrimePi[n]/(n-PrimePi[n])=1/Log[n]

> Solving for

> PrimePi[n]=n/(1+Log[n])

>

> I'm puzzled by this which I found this morning.

>

--

Respectfully, Roger L. Bagula

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