Re: What is the ratio of primes n converging with 2n+1 to prime ?

On Sep 24, 2008 Gerry Myerson wrote:
In article

<30549671.1222288788155.JavaMail.jakarta@xxxxxxxxxxxxx

forum.org>,
"Roman B. Binder" <rbinder@xxxxxxxxxxxxxxxx>
wrote:

I just wonder how it will happen with growing
value of n prime. Does 2n+1 always will have
a chance to be prime ?
For smallest primes from 2 to 101 the ratio is
next to 0.5 (exactly 14/29) :

This may be covered by the Bateman-Horn
conjectures,
q.v.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for
email)

Thank You very much.
I'll try to find this literature.

Best Regards
Ro-Bin
I used to look around this Bateman-Horn conjecture
but the most fitting are just Sophie Germain primes
or so called "safe primes".
There used to be found extremely big such primes,
what means, that there is not some limit because
of their size. Interested to me ratio could be
also of quite 0.5 ?
Anyhow once Sophie Germain used to develop
some proof of 1-st case FLT concerning with such
primes because of their mod3 and mod5 certain values
so I just find proof of 1-case of FLT for all
"safe primes" and for big part of 2-case for such primes...

With The Best Regards

Ro-Bin
.

Relevant Pages

  • Re: numbers n with large sum of divisors compared to n
    ... The ratio sigma/n can grow with n, ... Since the product over all primes ... This means that by adjusting the exponents of the prime factors of n, ... Using and the multiplicativity of sigma/n, ...
    (sci.math)
  • Re: JSH: Primes and politics, hero worship?
    ... there is no correction for the primes themselves so you are off ... remainder, so not using it introduces error by keeping that remainder ... pi/jsh: ratio pi / jsh ... that your approximation is going to get better as x approaches infinity (the ...
    (sci.math)
  • Re: Q: About number of primes with n digits?
    ... The next 21 primes are 2 digits in length. ... Will the ratio between terms converge? ... In your first statement, even if assuming the Riemann Hypothesis, ...
    (sci.math)
  • Re: Q: About number of primes with n digits?
    ... The next 21 primes are 2 digits in length. ... Will the ratio between terms converge? ... In your first statement, even if assuming the Riemann Hypothesis, ...
    (sci.math)
  • Re: Q: About number of primes with n digits?
    ... The next 21 primes are 2 digits in length. ... Will the ratio between terms converge? ... In your first statement, even if assuming the Riemann Hypothesis, ...
    (sci.math)