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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

9 votes
3 answers
2k views

Heuristic justification for Goldbach's conjecture

On the Wikipedia page of Goldbach's conjecture, a heuristic justification is given, which did not completely satisfy me. It roughly goes as follows: randomly define a subset integers in accord …
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  • 2,745
185 votes
11 answers
52k views

Knuth's intuition that Goldbach might be unprovable

Knuth's intuition that Goldbach's conjecture (every even number greater than 2 can be written as a sum of two primes) might be one of the statements that can neither be proved nor disproved really puz …
AgCl's user avatar
  • 2,745