On the sum of the reciprocals of the twin primes and the Brun constant
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I have this question related to the sum of the reciprocals of the twin primes:
how to explain that, for $x ge 3$, we have
$$ pi _{2}(x)=Oleft({frac{x(log log x)^{2}}{(log x)^{2}}}right).$$
Does this imply that the sum is finite? Thank you in advance.
Note that I have not found the paper of Brun.
prime-twins distribution-of-primes
edited Nov 23 at 12:40
amWhy
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asked Aug 11 at 19:59
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up vote
0
down vote
favorite
I have this question related to the sum of the reciprocals of the twin primes:
how to explain that, for $x ge 3$, we have
$$ pi _{2}(x)=Oleft({frac{x(log log x)^{2}}{(log x)^{2}}}right).$$
Does this imply that the sum is finite? Thank you in advance.
Note that I have not found the paper of Brun.
prime-twins distribution-of-primes
edited Nov 23 at 12:40
amWhy
191k28224439
asked Aug 11 at 19:59
Theory Nombre
1297
1
See here: artofproblemsolving.com/wiki/index.php?title=Brun%27s_constant
– Alex R.
Aug 11 at 22:34
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have this question related to the sum of the reciprocals of the twin primes:
how to explain that, for $x ge 3$, we have
$$ pi _{2}(x)=Oleft({frac{x(log log x)^{2}}{(log x)^{2}}}right).$$
Does this imply that the sum is finite? Thank you in advance.
Note that I have not found the paper of Brun.
prime-twins distribution-of-primes
edited Nov 23 at 12:40
amWhy
191k28224439
asked Aug 11 at 19:59
Theory Nombre
1297
I have this question related to the sum of the reciprocals of the twin primes:
how to explain that, for $x ge 3$, we have
$$ pi _{2}(x)=Oleft({frac{x(log log x)^{2}}{(log x)^{2}}}right).$$
Does this imply that the sum is finite? Thank you in advance.
Note that I have not found the paper of Brun.
prime-twins distribution-of-primes
prime-twins distribution-of-primes
edited Nov 23 at 12:40
amWhy
191k28224439
asked Aug 11 at 19:59
Theory Nombre
1297
edited Nov 23 at 12:40
amWhy
191k28224439
asked Aug 11 at 19:59
Theory Nombre
1297
edited Nov 23 at 12:40
amWhy
191k28224439
edited Nov 23 at 12:40
amWhy
191k28224439
edited Nov 23 at 12:40
amWhy
191k28224439
191k28224439
asked Aug 11 at 19:59
Theory Nombre
1297
asked Aug 11 at 19:59
Theory Nombre
1297
asked Aug 11 at 19:59
Theory Nombre
1297
1297
1
See here: artofproblemsolving.com/wiki/index.php?title=Brun%27s_constant
– Alex R.
Aug 11 at 22:34
add a comment |
1
See here: artofproblemsolving.com/wiki/index.php?title=Brun%27s_constant
– Alex R.
Aug 11 at 22:34
1
1
See here: artofproblemsolving.com/wiki/index.php?title=Brun%27s_constant
– Alex R.
Aug 11 at 22:34
See here: artofproblemsolving.com/wiki/index.php?title=Brun%27s_constant
– Alex R.
Aug 11 at 22:34
add a comment |
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See here: artofproblemsolving.com/wiki/index.php?title=Brun%27s_constant
– Alex R.
Aug 11 at 22:34