Gauss and $int frac{dn}{log n}$
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In [1], page 2, Edwards shows a tabulated table by Gauss, for $x$ (distinct and uniformly distributed values from $5cdot 10^5$ to $3cdot 10^6$), the count of primes$<x$, the symbol $int frac{dn}{log n}$ and differences of previous computed quantities. In the following page the author discusses what might have understood Gauss by this amount $int dn/log n$. I know a standard topic in numerical analysis: Gauss quadratures. On page 2 is it also noted that Gauss knew the average of the density of prime numbers, and tabulations of primes that were published, thus I imagine that he computed using these informations the first column, this is the count of primes$<x$.
But I'm not sure what was the method for the second column, the symbol $int frac{dn}{log n}$. For this reason I have the following question:
Question. How were these quantities $int frac{dn}{log n}$ computed by Gauss? If you can give some detail, better.
References:
[1] Harold M. Edwards, Riemann's Zeta Function, Dover (edition) 2001.
math-history
asked Aug 7 '15 at 8:31
user243301user243301
1
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$begingroup$
In [1], page 2, Edwards shows a tabulated table by Gauss, for $x$ (distinct and uniformly distributed values from $5cdot 10^5$ to $3cdot 10^6$), the count of primes$<x$, the symbol $int frac{dn}{log n}$ and differences of previous computed quantities. In the following page the author discusses what might have understood Gauss by this amount $int dn/log n$. I know a standard topic in numerical analysis: Gauss quadratures. On page 2 is it also noted that Gauss knew the average of the density of prime numbers, and tabulations of primes that were published, thus I imagine that he computed using these informations the first column, this is the count of primes$<x$.
But I'm not sure what was the method for the second column, the symbol $int frac{dn}{log n}$. For this reason I have the following question:
Question. How were these quantities $int frac{dn}{log n}$ computed by Gauss? If you can give some detail, better.
References:
[1] Harold M. Edwards, Riemann's Zeta Function, Dover (edition) 2001.
math-history
asked Aug 7 '15 at 8:31
user243301user243301
1
$endgroup$
add a comment |
$begingroup$
In [1], page 2, Edwards shows a tabulated table by Gauss, for $x$ (distinct and uniformly distributed values from $5cdot 10^5$ to $3cdot 10^6$), the count of primes$<x$, the symbol $int frac{dn}{log n}$ and differences of previous computed quantities. In the following page the author discusses what might have understood Gauss by this amount $int dn/log n$. I know a standard topic in numerical analysis: Gauss quadratures. On page 2 is it also noted that Gauss knew the average of the density of prime numbers, and tabulations of primes that were published, thus I imagine that he computed using these informations the first column, this is the count of primes$<x$.
But I'm not sure what was the method for the second column, the symbol $int frac{dn}{log n}$. For this reason I have the following question:
Question. How were these quantities $int frac{dn}{log n}$ computed by Gauss? If you can give some detail, better.
References:
[1] Harold M. Edwards, Riemann's Zeta Function, Dover (edition) 2001.
math-history
asked Aug 7 '15 at 8:31
user243301user243301
1
$endgroup$
In [1], page 2, Edwards shows a tabulated table by Gauss, for $x$ (distinct and uniformly distributed values from $5cdot 10^5$ to $3cdot 10^6$), the count of primes$<x$, the symbol $int frac{dn}{log n}$ and differences of previous computed quantities. In the following page the author discusses what might have understood Gauss by this amount $int dn/log n$. I know a standard topic in numerical analysis: Gauss quadratures. On page 2 is it also noted that Gauss knew the average of the density of prime numbers, and tabulations of primes that were published, thus I imagine that he computed using these informations the first column, this is the count of primes$<x$.
But I'm not sure what was the method for the second column, the symbol $int frac{dn}{log n}$. For this reason I have the following question:
Question. How were these quantities $int frac{dn}{log n}$ computed by Gauss? If you can give some detail, better.
References:
[1] Harold M. Edwards, Riemann's Zeta Function, Dover (edition) 2001.
math-history
math-history
asked Aug 7 '15 at 8:31
user243301user243301
1
asked Aug 7 '15 at 8:31
user243301user243301
1
edited Dec 25 '18 at 16:16
user243301
asked Aug 7 '15 at 8:31
user243301user243301
1
asked Aug 7 '15 at 8:31
user243301user243301
1
asked Aug 7 '15 at 8:31
user243301user243301
1
1
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I believe he used the equivalent
$$
pi(x) approx frac{x}{log x},
$$
and he had access to massive logarithm tables computed by hand by his peers.
answered Dec 17 '18 at 11:17
KlangenKlangen
1,75111334
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$begingroup$
I believe he used the equivalent
$$
pi(x) approx frac{x}{log x},
$$
and he had access to massive logarithm tables computed by hand by his peers.
answered Dec 17 '18 at 11:17
KlangenKlangen
1,75111334
$endgroup$
add a comment |
$begingroup$
I believe he used the equivalent
$$
pi(x) approx frac{x}{log x},
$$
and he had access to massive logarithm tables computed by hand by his peers.
answered Dec 17 '18 at 11:17
KlangenKlangen
1,75111334
$endgroup$
add a comment |
$begingroup$
I believe he used the equivalent
$$
pi(x) approx frac{x}{log x},
$$
and he had access to massive logarithm tables computed by hand by his peers.
answered Dec 17 '18 at 11:17
KlangenKlangen
1,75111334
$endgroup$
I believe he used the equivalent
$$
pi(x) approx frac{x}{log x},
$$
and he had access to massive logarithm tables computed by hand by his peers.
answered Dec 17 '18 at 11:17
KlangenKlangen
1,75111334
answered Dec 17 '18 at 11:17
KlangenKlangen
1,75111334
answered Dec 17 '18 at 11:17
KlangenKlangen
1,75111334
answered Dec 17 '18 at 11:17
KlangenKlangen
1,75111334
1,75111334
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