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Goldbach’s conjecture in max-algebra


The Goldbach conjecture is one of the best known open problems in number theory. It claims that every even integer greater than 2 can be written as the sum of two primes. The present paper formulates a max-algebraic claim that is equivalent to Goldbach’s conjecture. The max-algebraic analogue allows examination of the conjecture by the methods of max-algebra. A max-algebra is an algebraic structure in which classical addition \(+\) and multiplication \(\times \) are replaced by the operations maximum \(\oplus \) and addition \(\otimes \), in other words \(a\oplus b=\max \{a,b\}\) and \(a\otimes b=a+b\).

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Correspondence to Peter Szabó.

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Szabó, P. Goldbach’s conjecture in max-algebra. Comput Manag Sci 14, 81–89 (2017).

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  • Max-algebra
  • Triangular Toeplitz matrix
  • Goldbach’s conjecture