Recently we talked about the Riemann hypothesis in class, and yesterday I stumbled across the Goldbach conjectures. I realized there are quite a few theories that assert a particular property to all numbers of a specific form (greater than some n), which have been confirmed for the first gazillion numbers. Yet that is not sufficient proof. (Of course, some of them have been proven.)

So out of interest: Are there any such theories that remain valid for a wide range of numbers and then suddenly break off?

  • $\begingroup$ By number theories, do you mean hypotheses or laws for natural numbers? $\endgroup$
    – Ilya
    Jul 28 '14 at 11:43
  • $\begingroup$ Well, hypotheses, since laws should hold for all natural numbers per definition, right? $\endgroup$ Jul 28 '14 at 11:47
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    $\begingroup$ Pólya conjecture comes to mind $\endgroup$ Jul 28 '14 at 11:48
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    $\begingroup$ Also, this thread has some examples of "almost true" statements in general, not only for number theory $\endgroup$ Jul 28 '14 at 11:51
  • $\begingroup$ See also mathoverflow.net/questions/15444/… $\endgroup$ Jul 28 '14 at 12:36

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