I want to collect a list of Goldbach's other conjectures












0














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







share|cite|improve this question




















  • 2




    You can find all of Goldbach's correspondence with Euler at eulerarchive.maa.org//correspondence/correspondents/… (but it's all in Latin).
    – Gerry Myerson
    Jun 22 '18 at 10:13










  • Most of it is in German, actually. The English version (along with the originals plus detailed comments) is available at edoc.unibas.ch/58842
    – franz lemmermeyer
    Dec 5 '18 at 18:23


















0














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







share|cite|improve this question




















  • 2




    You can find all of Goldbach's correspondence with Euler at eulerarchive.maa.org//correspondence/correspondents/… (but it's all in Latin).
    – Gerry Myerson
    Jun 22 '18 at 10:13










  • Most of it is in German, actually. The English version (along with the originals plus detailed comments) is available at edoc.unibas.ch/58842
    – franz lemmermeyer
    Dec 5 '18 at 18:23
















0












0








0


1





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







share|cite|improve this question















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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jun 22 '18 at 10:03









José Carlos Santos

152k22123225




152k22123225










asked Jun 22 '18 at 9:45









DERDER

1,648918




1,648918








  • 2




    You can find all of Goldbach's correspondence with Euler at eulerarchive.maa.org//correspondence/correspondents/… (but it's all in Latin).
    – Gerry Myerson
    Jun 22 '18 at 10:13










  • Most of it is in German, actually. The English version (along with the originals plus detailed comments) is available at edoc.unibas.ch/58842
    – franz lemmermeyer
    Dec 5 '18 at 18:23
















  • 2




    You can find all of Goldbach's correspondence with Euler at eulerarchive.maa.org//correspondence/correspondents/… (but it's all in Latin).
    – Gerry Myerson
    Jun 22 '18 at 10:13










  • Most of it is in German, actually. The English version (along with the originals plus detailed comments) is available at edoc.unibas.ch/58842
    – franz lemmermeyer
    Dec 5 '18 at 18:23










2




2




You can find all of Goldbach's correspondence with Euler at eulerarchive.maa.org//correspondence/correspondents/… (but it's all in Latin).
– Gerry Myerson
Jun 22 '18 at 10:13




You can find all of Goldbach's correspondence with Euler at eulerarchive.maa.org//correspondence/correspondents/… (but it's all in Latin).
– Gerry Myerson
Jun 22 '18 at 10:13












Most of it is in German, actually. The English version (along with the originals plus detailed comments) is available at edoc.unibas.ch/58842
– franz lemmermeyer
Dec 5 '18 at 18:23






Most of it is in German, actually. The English version (along with the originals plus detailed comments) is available at edoc.unibas.ch/58842
– franz lemmermeyer
Dec 5 '18 at 18:23












3 Answers
3






active

oldest

votes


















5














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.






share|cite|improve this answer





























    1














    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).






    share|cite|improve this answer





























      0














      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







      share|cite|improve this answer























        Your Answer





        StackExchange.ifUsing("editor", function () {
        return StackExchange.using("mathjaxEditing", function () {
        StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
        StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
        });
        });
        }, "mathjax-editing");

        StackExchange.ready(function() {
        var channelOptions = {
        tags: "".split(" "),
        id: "69"
        };
        initTagRenderer("".split(" "), "".split(" "), channelOptions);

        StackExchange.using("externalEditor", function() {
        // Have to fire editor after snippets, if snippets enabled
        if (StackExchange.settings.snippets.snippetsEnabled) {
        StackExchange.using("snippets", function() {
        createEditor();
        });
        }
        else {
        createEditor();
        }
        });

        function createEditor() {
        StackExchange.prepareEditor({
        heartbeatType: 'answer',
        autoActivateHeartbeat: false,
        convertImagesToLinks: true,
        noModals: true,
        showLowRepImageUploadWarning: true,
        reputationToPostImages: 10,
        bindNavPrevention: true,
        postfix: "",
        imageUploader: {
        brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
        contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
        allowUrls: true
        },
        noCode: true, onDemand: true,
        discardSelector: ".discard-answer"
        ,immediatelyShowMarkdownHelp:true
        });


        }
        });














        draft saved

        draft discarded


















        StackExchange.ready(
        function () {
        StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2828281%2fi-want-to-collect-a-list-of-goldbachs-other-conjectures%23new-answer', 'question_page');
        }
        );

        Post as a guest















        Required, but never shown

























        3 Answers
        3






        active

        oldest

        votes








        3 Answers
        3






        active

        oldest

        votes









        active

        oldest

        votes






        active

        oldest

        votes









        5














        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.






        share|cite|improve this answer


























          5














          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.






          share|cite|improve this answer
























            5












            5








            5






            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.






            share|cite|improve this answer












            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.







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Jun 22 '18 at 9:51









            José Carlos SantosJosé Carlos Santos

            152k22123225




            152k22123225























                1














                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).






                share|cite|improve this answer


























                  1














                  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).






                  share|cite|improve this answer
























                    1












                    1








                    1






                    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).






                    share|cite|improve this answer












                    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).







                    share|cite|improve this answer












                    share|cite|improve this answer



                    share|cite|improve this answer










                    answered Jun 22 '18 at 18:42









                    Dietrich BurdeDietrich Burde

                    78.1k64386




                    78.1k64386























                        0














                        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







                        share|cite|improve this answer




























                          0














                          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







                          share|cite|improve this answer


























                            0












                            0








                            0






                            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







                            share|cite|improve this answer














                            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








                            share|cite|improve this answer














                            share|cite|improve this answer



                            share|cite|improve this answer








                            answered Dec 5 '18 at 9:46


























                            community wiki





                            Brahadeesh































                                draft saved

                                draft discarded




















































                                Thanks for contributing an answer to Mathematics Stack Exchange!


                                • Please be sure to answer the question. Provide details and share your research!

                                But avoid …



                                • Asking for help, clarification, or responding to other answers.

                                • Making statements based on opinion; back them up with references or personal experience.


                                Use MathJax to format equations. MathJax reference.


                                To learn more, see our tips on writing great answers.





                                Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


                                Please pay close attention to the following guidance:


                                • Please be sure to answer the question. Provide details and share your research!

                                But avoid …



                                • Asking for help, clarification, or responding to other answers.

                                • Making statements based on opinion; back them up with references or personal experience.


                                To learn more, see our tips on writing great answers.




                                draft saved


                                draft discarded














                                StackExchange.ready(
                                function () {
                                StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2828281%2fi-want-to-collect-a-list-of-goldbachs-other-conjectures%23new-answer', 'question_page');
                                }
                                );

                                Post as a guest















                                Required, but never shown





















































                                Required, but never shown














                                Required, but never shown












                                Required, but never shown







                                Required, but never shown

































                                Required, but never shown














                                Required, but never shown












                                Required, but never shown







                                Required, but never shown







                                -

                                Popular posts from this blog

                                Berounka

                                Image
                                Berounka.mw-parser-output .entete.map{background-image:url("//upload.wikimedia.org/wikipedia/commons/7/7a/Picto_infobox_map.png")} Caractéristiques Longueur 139  km Bassin 8 861  km 2 Bassin collecteur Elbe Débit moyen ? Cours Source Confluence de la Mže et de la Radbuza · Localisation Pilsen · Altitude 305  m · Coordonnées 49° 45′ 13″ N, 13° 23′ 24″ E Confluence Vltava · Localisation Prague · Altitude 187  m · Coordonnées 49° 59′ 43″ N, 14° 24′ 04″ E Géographie Pays traversés   République tchèque modifier   La Berounka est une rivière de la République tchèque. Elle porte le nom de Mže depuis sa source en Allemagne près de la frontière jusqu'à sa confluence avec la Radbuza à Plzeň. Elle continue ensuite sous le nom de Berounka jusqu'à sa confluence avec la Vltava, près de Prague. La rivière est une destination prisée pour les amateurs de canoë, qui appréc...
                                Read more

                                Sphinx de Gizeh

                                Image
                                Pour les articles homonymes, voir Sphinx. Sphinx de Gizeh.mw-parser-output .entete.egypte-antique{background-image:url("//upload.wikimedia.org/wikipedia/commons/c/cc/Picto_infobox_ancient_Egypt.png")} Site d'Égypte antique Le visage du sphinx de Gizeh. Noms en arabe أبو الهول , Abou al-Hôl Localisation Région Basse-Égypte Coordonnées 29° 58′ 31″ nord, 31° 08′ 16″ est Géolocalisation sur la carte : Égypte Sphinx de Gizeh modifier   Le sphinx de Gizeh est la statue thérianthrope qui se dresse devant les grandes pyramides du plateau de Gizeh, en Basse-Égypte. Sculpture monumentale monolithique la plus grande du monde [ 1 ] avec 73,5 mètres de longueur, 14 mètres de largeur et 20,22 mètres de hauteur, elle représente un sphinx couchant. Réalisée vers -2500, elle serait attribuée à Djédefrê, l'un des pharaons de la IV e  dynastie, représentant son père le pharaon Khéops. Sommaire 1 Étymologie 2 Desc...
                                Read more

                                Different font size/position of beamer's navigation symbols template's content depending on regular/plain...

                                Image
                                3 Let's suppose I'd like to divert the navigation symbols template (e.g. in order replace them by the frame numbers, see this bug report ;) I would be facing troubles regarding the font size/position, depending on regular/plain frames, as shown by the following MCE. How could I get rid of these troubles? documentclass{beamer} usetheme{PaloAlto} setbeamertemplate{navigation symbols}{insertframenumber/inserttotalframenumber} begin{document} begin{frame} frametitle{A regular frame} end{frame} begin{frame}[plain] frametitle{A plain frame} end{frame} end{document} beamer header-footer share | improve this question asked Dec 10 '18 a...
                                Read more