Is this a valid function for number of prime pairs for n=2p and p is prime and n gets large?
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For even integer n=2p where p is a prime number, as n gets large, does the number of prime pairs P(n) approaches the following equation:
$P(n) = (frac{n}{2})(1-2W(l(sqrt n))$
where l(√n) is the largest prime number less than √n, and W(x) is defined as the following function:
$W(x) = sum_{p=3}^{x} frac{1}{p}left(prod_{q=3}^{l(p)} frac{(q-2)}{q}right)$
where the sum and products are over prime numbers and x is a prime number.
A prime pair of n is a pair (p1,p2) such that p1 and p2 are prime and p1+p2=n.
number-theory
asked Nov 21 at 14:18
temp watts
42
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up vote
-1
down vote
favorite
For even integer n=2p where p is a prime number, as n gets large, does the number of prime pairs P(n) approaches the following equation:
$P(n) = (frac{n}{2})(1-2W(l(sqrt n))$
where l(√n) is the largest prime number less than √n, and W(x) is defined as the following function:
$W(x) = sum_{p=3}^{x} frac{1}{p}left(prod_{q=3}^{l(p)} frac{(q-2)}{q}right)$
where the sum and products are over prime numbers and x is a prime number.
A prime pair of n is a pair (p1,p2) such that p1 and p2 are prime and p1+p2=n.
number-theory
asked Nov 21 at 14:18
temp watts
42
Welcome to MSE. Please show more effort and more people would be willing to answer. :)
– Kyky
Nov 21 at 14:19
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
For even integer n=2p where p is a prime number, as n gets large, does the number of prime pairs P(n) approaches the following equation:
$P(n) = (frac{n}{2})(1-2W(l(sqrt n))$
where l(√n) is the largest prime number less than √n, and W(x) is defined as the following function:
$W(x) = sum_{p=3}^{x} frac{1}{p}left(prod_{q=3}^{l(p)} frac{(q-2)}{q}right)$
where the sum and products are over prime numbers and x is a prime number.
A prime pair of n is a pair (p1,p2) such that p1 and p2 are prime and p1+p2=n.
number-theory
asked Nov 21 at 14:18
temp watts
42
For even integer n=2p where p is a prime number, as n gets large, does the number of prime pairs P(n) approaches the following equation:
$P(n) = (frac{n}{2})(1-2W(l(sqrt n))$
where l(√n) is the largest prime number less than √n, and W(x) is defined as the following function:
$W(x) = sum_{p=3}^{x} frac{1}{p}left(prod_{q=3}^{l(p)} frac{(q-2)}{q}right)$
where the sum and products are over prime numbers and x is a prime number.
A prime pair of n is a pair (p1,p2) such that p1 and p2 are prime and p1+p2=n.
number-theory
number-theory
asked Nov 21 at 14:18
temp watts
42
asked Nov 21 at 14:18
temp watts
42
edited Nov 21 at 14:19
asked Nov 21 at 14:18
temp watts
42
asked Nov 21 at 14:18
temp watts
42
asked Nov 21 at 14:18
temp watts
42
42
Welcome to MSE. Please show more effort and more people would be willing to answer. :)
– Kyky
Nov 21 at 14:19
add a comment |
Welcome to MSE. Please show more effort and more people would be willing to answer. :)
– Kyky
Nov 21 at 14:19
Welcome to MSE. Please show more effort and more people would be willing to answer. :)
– Kyky
Nov 21 at 14:19
Welcome to MSE. Please show more effort and more people would be willing to answer. :)
– Kyky
Nov 21 at 14:19
add a comment |
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Welcome to MSE. Please show more effort and more people would be willing to answer. :)
– Kyky
Nov 21 at 14:19