## RE reciprocal consecutive primes (typo)

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• ... From: Jose Ramón Brox q/p 7. ... I mean it s a SUFFICIENT condition.
Message 1 of 3 , Nov 2 3:33 PM
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----- Original Message -----
From: "Jose Ramón Brox" <ambroxius@...>

q/p < 3/2 is a simpler necessary condition that seems to hold if p>7.

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I mean it's a SUFFICIENT condition. If q/p < 3/2, then by the inequalities developed in
the former email, we got that 1/p < 1/q + 1/r.

Regards. Jose Brox.
• ... From: Jose Ramón Brox Consider b = a-1, then we have m*n = (p+a)(p-b) = (p+a)(p-a+1) = p^2 +p-a(a+1) ... The final equality should
Message 2 of 3 , Nov 3 4:03 AM
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----- Original Message -----
From: "Jose Ramón Brox" <ambroxius@...>

Consider b = a-1, then we have

m*n = (p+a)(p-b) = (p+a)(p-a+1) = p^2 +p-a(a+1)

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The final equality should read p^2 + p -a(a-1)

Jose Brox
• Gauss-Legendre conjectured that the prime counting function of x is similar to x/ln(x). (Or more specifically that as x approaches infinity: pi(x)/(x/ln(x)) -
Message 3 of 3 , Nov 3 8:38 AM
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Gauss-Legendre conjectured that the prime counting
function of x is similar to x/ln(x).
(Or more specifically that as x approaches infinity:
pi(x)/(x/ln(x)) -> 1)

Are there other functions in number theory that are
similar to the function:
y = x/ln(x)?

Specifically I'm studying a phenomenon that appears to
resemble:
y = x/ln(x+c)

- Jeremy
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