I want to collect a list of Goldbach's other conjectures
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I want to collect a list of Goldbach's other conjectures. I konw only two conjectures: The first one is the famous statement on writting an even number as the sum of two primes and the other one is about expressing an even number by $3$ primes.
number-theory math-history big-list
edited Jun 22 '18 at 10:03
José Carlos Santos
156k22125227
asked Jun 22 '18 at 9:45
DERDER
1,648918
$endgroup$
add a comment |
$begingroup$
I want to collect a list of Goldbach's other conjectures. I konw only two conjectures: The first one is the famous statement on writting an even number as the sum of two primes and the other one is about expressing an even number by $3$ primes.
number-theory math-history big-list
edited Jun 22 '18 at 10:03
José Carlos Santos
156k22125227
asked Jun 22 '18 at 9:45
DERDER
1,648918
$endgroup$
2
$begingroup$
You can find all of Goldbach's correspondence with Euler at eulerarchive.maa.org//correspondence/correspondents/… (but it's all in Latin).
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– Gerry Myerson
Jun 22 '18 at 10:13
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Most of it is in German, actually. The English version (along with the originals plus detailed comments) is available at edoc.unibas.ch/58842
$endgroup$
– franz lemmermeyer
Dec 5 '18 at 18:23
add a comment |
$begingroup$
I want to collect a list of Goldbach's other conjectures. I konw only two conjectures: The first one is the famous statement on writting an even number as the sum of two primes and the other one is about expressing an even number by $3$ primes.
number-theory math-history big-list
edited Jun 22 '18 at 10:03
José Carlos Santos
156k22125227
asked Jun 22 '18 at 9:45
DERDER
1,648918
$endgroup$
I want to collect a list of Goldbach's other conjectures. I konw only two conjectures: The first one is the famous statement on writting an even number as the sum of two primes and the other one is about expressing an even number by $3$ primes.
number-theory math-history big-list
number-theory math-history big-list
edited Jun 22 '18 at 10:03
José Carlos Santos
156k22125227
asked Jun 22 '18 at 9:45
DERDER
1,648918
edited Jun 22 '18 at 10:03
José Carlos Santos
156k22125227
asked Jun 22 '18 at 9:45
DERDER
1,648918
edited Jun 22 '18 at 10:03
José Carlos Santos
156k22125227
edited Jun 22 '18 at 10:03
José Carlos Santos
156k22125227
edited Jun 22 '18 at 10:03
José Carlos Santos
156k22125227
156k22125227
asked Jun 22 '18 at 9:45
DERDER
1,648918
asked Jun 22 '18 at 9:45
DERDER
1,648918
asked Jun 22 '18 at 9:45
DERDER
1,648918
1,648918
2
$begingroup$
You can find all of Goldbach's correspondence with Euler at eulerarchive.maa.org//correspondence/correspondents/… (but it's all in Latin).
$endgroup$
– Gerry Myerson
Jun 22 '18 at 10:13
$begingroup$
Most of it is in German, actually. The English version (along with the originals plus detailed comments) is available at edoc.unibas.ch/58842
$endgroup$
– franz lemmermeyer
Dec 5 '18 at 18:23
add a comment |
2
$begingroup$
You can find all of Goldbach's correspondence with Euler at eulerarchive.maa.org//correspondence/correspondents/… (but it's all in Latin).
$endgroup$
– Gerry Myerson
Jun 22 '18 at 10:13
$begingroup$
Most of it is in German, actually. The English version (along with the originals plus detailed comments) is available at edoc.unibas.ch/58842
$endgroup$
– franz lemmermeyer
Dec 5 '18 at 18:23
2
2
$begingroup$
You can find all of Goldbach's correspondence with Euler at eulerarchive.maa.org//correspondence/correspondents/… (but it's all in Latin).
$endgroup$
– Gerry Myerson
Jun 22 '18 at 10:13
$begingroup$
You can find all of Goldbach's correspondence with Euler at eulerarchive.maa.org//correspondence/correspondents/… (but it's all in Latin).
$endgroup$
– Gerry Myerson
Jun 22 '18 at 10:13
$begingroup$
Most of it is in German, actually. The English version (along with the originals plus detailed comments) is available at edoc.unibas.ch/58842
$endgroup$
– franz lemmermeyer
Dec 5 '18 at 18:23
$begingroup$
Most of it is in German, actually. The English version (along with the originals plus detailed comments) is available at edoc.unibas.ch/58842
$endgroup$
– franz lemmermeyer
Dec 5 '18 at 18:23
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
I don't know which conjecture is that about expressing an even number by $3$ primes, but Goldbach also conjectured, in a letter to Euler written in 1752, that every odd number can be written as $2n^2+p$, with $p$ prime. Euler checked it for every number up to $2,500$. It turns out that the conjecture is false: in 1856, Moritz A. Stern, a professor of mathematics at Göttingen, found two numbers which could not be written as twice a square plus a prime, namely $5,777$ and $5,993$. These seem to be the only known counter-examples to this conjecture.
answered Jun 22 '18 at 9:51
José Carlos SantosJosé Carlos Santos
156k22125227
$endgroup$
add a comment |
$begingroup$
Actually, there is another "Goldbach conjecture" which Goldbach was able to prove himself:
in $1752$, Goldbach showed that no polynomial with integer coefficients can give a prime for all integer values (Nagell 1951, p. 65; Hardy and Wright 1979, pp. 18 and 22).
answered Jun 22 '18 at 18:42
Dietrich BurdeDietrich Burde
78.4k64386
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add a comment |
$begingroup$
I am turning @GerryMyerson's comment into an answer because it is useful and relevant to the question.
You can find all of Goldbach's correspondence with Euler at http://eulerarchive.maa.org//correspondence/correspondents/Goldbach.html (but it's all in Latin).
From the Publication Information on the website:
167 letters from the Euler-Goldbach Correspondence were published by P.H. Fuss in his Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle . The letters below all came from Fuss' book. Unfortunately, Fuss often excised the personal part of the correspondence, and published only the scientific material. A complete set of the correspondence will have to wait until the publication of the appropriate volume of the Opera Omnia
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I don't know which conjecture is that about expressing an even number by $3$ primes, but Goldbach also conjectured, in a letter to Euler written in 1752, that every odd number can be written as $2n^2+p$, with $p$ prime. Euler checked it for every number up to $2,500$. It turns out that the conjecture is false: in 1856, Moritz A. Stern, a professor of mathematics at Göttingen, found two numbers which could not be written as twice a square plus a prime, namely $5,777$ and $5,993$. These seem to be the only known counter-examples to this conjecture.
answered Jun 22 '18 at 9:51
José Carlos SantosJosé Carlos Santos
156k22125227
$endgroup$
add a comment |
$begingroup$
I don't know which conjecture is that about expressing an even number by $3$ primes, but Goldbach also conjectured, in a letter to Euler written in 1752, that every odd number can be written as $2n^2+p$, with $p$ prime. Euler checked it for every number up to $2,500$. It turns out that the conjecture is false: in 1856, Moritz A. Stern, a professor of mathematics at Göttingen, found two numbers which could not be written as twice a square plus a prime, namely $5,777$ and $5,993$. These seem to be the only known counter-examples to this conjecture.
answered Jun 22 '18 at 9:51
José Carlos SantosJosé Carlos Santos
156k22125227
$endgroup$
add a comment |
$begingroup$
I don't know which conjecture is that about expressing an even number by $3$ primes, but Goldbach also conjectured, in a letter to Euler written in 1752, that every odd number can be written as $2n^2+p$, with $p$ prime. Euler checked it for every number up to $2,500$. It turns out that the conjecture is false: in 1856, Moritz A. Stern, a professor of mathematics at Göttingen, found two numbers which could not be written as twice a square plus a prime, namely $5,777$ and $5,993$. These seem to be the only known counter-examples to this conjecture.
answered Jun 22 '18 at 9:51
José Carlos SantosJosé Carlos Santos
156k22125227
$endgroup$
I don't know which conjecture is that about expressing an even number by $3$ primes, but Goldbach also conjectured, in a letter to Euler written in 1752, that every odd number can be written as $2n^2+p$, with $p$ prime. Euler checked it for every number up to $2,500$. It turns out that the conjecture is false: in 1856, Moritz A. Stern, a professor of mathematics at Göttingen, found two numbers which could not be written as twice a square plus a prime, namely $5,777$ and $5,993$. These seem to be the only known counter-examples to this conjecture.
answered Jun 22 '18 at 9:51
José Carlos SantosJosé Carlos Santos
156k22125227
answered Jun 22 '18 at 9:51
José Carlos SantosJosé Carlos Santos
156k22125227
answered Jun 22 '18 at 9:51
José Carlos SantosJosé Carlos Santos
156k22125227
answered Jun 22 '18 at 9:51
José Carlos SantosJosé Carlos Santos
156k22125227
156k22125227
add a comment |
add a comment |
$begingroup$
Actually, there is another "Goldbach conjecture" which Goldbach was able to prove himself:
in $1752$, Goldbach showed that no polynomial with integer coefficients can give a prime for all integer values (Nagell 1951, p. 65; Hardy and Wright 1979, pp. 18 and 22).
answered Jun 22 '18 at 18:42
Dietrich BurdeDietrich Burde
78.4k64386
$endgroup$
add a comment |
$begingroup$
Actually, there is another "Goldbach conjecture" which Goldbach was able to prove himself:
in $1752$, Goldbach showed that no polynomial with integer coefficients can give a prime for all integer values (Nagell 1951, p. 65; Hardy and Wright 1979, pp. 18 and 22).
answered Jun 22 '18 at 18:42
Dietrich BurdeDietrich Burde
78.4k64386
$endgroup$
add a comment |
$begingroup$
Actually, there is another "Goldbach conjecture" which Goldbach was able to prove himself:
in $1752$, Goldbach showed that no polynomial with integer coefficients can give a prime for all integer values (Nagell 1951, p. 65; Hardy and Wright 1979, pp. 18 and 22).
answered Jun 22 '18 at 18:42
Dietrich BurdeDietrich Burde
78.4k64386
$endgroup$
Actually, there is another "Goldbach conjecture" which Goldbach was able to prove himself:
in $1752$, Goldbach showed that no polynomial with integer coefficients can give a prime for all integer values (Nagell 1951, p. 65; Hardy and Wright 1979, pp. 18 and 22).
answered Jun 22 '18 at 18:42
Dietrich BurdeDietrich Burde
78.4k64386
answered Jun 22 '18 at 18:42
Dietrich BurdeDietrich Burde
78.4k64386
answered Jun 22 '18 at 18:42
Dietrich BurdeDietrich Burde
78.4k64386
answered Jun 22 '18 at 18:42
Dietrich BurdeDietrich Burde
78.4k64386
78.4k64386
add a comment |
add a comment |
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I am turning @GerryMyerson's comment into an answer because it is useful and relevant to the question.
You can find all of Goldbach's correspondence with Euler at http://eulerarchive.maa.org//correspondence/correspondents/Goldbach.html (but it's all in Latin).
From the Publication Information on the website:
167 letters from the Euler-Goldbach Correspondence were published by P.H. Fuss in his Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle . The letters below all came from Fuss' book. Unfortunately, Fuss often excised the personal part of the correspondence, and published only the scientific material. A complete set of the correspondence will have to wait until the publication of the appropriate volume of the Opera Omnia
$endgroup$
add a comment |
$begingroup$
I am turning @GerryMyerson's comment into an answer because it is useful and relevant to the question.
You can find all of Goldbach's correspondence with Euler at http://eulerarchive.maa.org//correspondence/correspondents/Goldbach.html (but it's all in Latin).
From the Publication Information on the website:
167 letters from the Euler-Goldbach Correspondence were published by P.H. Fuss in his Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle . The letters below all came from Fuss' book. Unfortunately, Fuss often excised the personal part of the correspondence, and published only the scientific material. A complete set of the correspondence will have to wait until the publication of the appropriate volume of the Opera Omnia
$endgroup$
add a comment |
$begingroup$
I am turning @GerryMyerson's comment into an answer because it is useful and relevant to the question.
You can find all of Goldbach's correspondence with Euler at http://eulerarchive.maa.org//correspondence/correspondents/Goldbach.html (but it's all in Latin).
From the Publication Information on the website:
167 letters from the Euler-Goldbach Correspondence were published by P.H. Fuss in his Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle . The letters below all came from Fuss' book. Unfortunately, Fuss often excised the personal part of the correspondence, and published only the scientific material. A complete set of the correspondence will have to wait until the publication of the appropriate volume of the Opera Omnia
$endgroup$
I am turning @GerryMyerson's comment into an answer because it is useful and relevant to the question.
You can find all of Goldbach's correspondence with Euler at http://eulerarchive.maa.org//correspondence/correspondents/Goldbach.html (but it's all in Latin).
From the Publication Information on the website:
167 letters from the Euler-Goldbach Correspondence were published by P.H. Fuss in his Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle . The letters below all came from Fuss' book. Unfortunately, Fuss often excised the personal part of the correspondence, and published only the scientific material. A complete set of the correspondence will have to wait until the publication of the appropriate volume of the Opera Omnia
answered Dec 5 '18 at 9:46
community wiki
Brahadeesh
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$begingroup$
You can find all of Goldbach's correspondence with Euler at eulerarchive.maa.org//correspondence/correspondents/… (but it's all in Latin).
$endgroup$
– Gerry Myerson
Jun 22 '18 at 10:13
$begingroup$
Most of it is in German, actually. The English version (along with the originals plus detailed comments) is available at edoc.unibas.ch/58842
$endgroup$
– franz lemmermeyer
Dec 5 '18 at 18:23