## PNT and an attempt to persuade

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• I Have a mathematician friend and I am trying to convince him of the following: Take P(m) to be the set of primes less than the square root of an integer n.
Message 1 of 2 , Mar 17, 2008
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I Have a mathematician friend and I am trying to convince him of the
following:

Take P(m) to be the set of primes less than the square root of an
integer n.
Take a(m) to be their product.
Consider a matrix in which members of P(m) index rows and in which
each column that is defined as 'unoccupied' is on that does not index
a multiple of a member of P(m).
Take the number of unoccupied columns in an interval of length a(m) to
be u.
By the proof of the Prime Number Theorem, as n increases
pi(n)converges on u*n/a(m).

How can I do this?

Cheers.
Tom
• On Tuesday, March 18, 2008 8:09 AM, gulland68 wrote in primenumbers: TG Consider a matrix in which members of P(m) index rows and in which each column that
Message 2 of 2 , Mar 19, 2008
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On Tuesday, March 18, 2008 8:09 AM, gulland68 wrote in primenumbers:

TG>> Consider a matrix in which members of P(m) index rows and in which each
column that is defined as 'unoccupied' is on that does not index a multiple
of a member of P(m). . How can I do this? <<TG

Tom
====
See if this matrix for generating the primes helps:

http://alixcomsi.com/A_Minimal_Prime.htm

Bhup
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