An elementary heuristic for Hardy-Littlewood extended Goldbach's conjecture
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2015
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| _version_ | 1866929633570586624 |
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| author | Táfula, Christian |
| author_facet | Táfula, Christian |
| contents | The goal of this paper is to describe an elementary combinatorial heuristic that predicts Hardy and Littlewood's extended Goldbach's conjecture. We examine common features of other heuristics in additive prime number theory, such as Cramér's model and density-type arguments, both of which our heuristic draws from. Apart from the prime number theorem, our argument is entirely elementary, in the sense of not involving complex analysis. The idea is to model sums of two primes by a hypergeometric probability distribution, and then draw heuristic conclusions from its concentration behavior, which follows from Hoeffding-type bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1508_05702 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | An elementary heuristic for Hardy-Littlewood extended Goldbach's conjecture Táfula, Christian Number Theory Combinatorics 11P32 The goal of this paper is to describe an elementary combinatorial heuristic that predicts Hardy and Littlewood's extended Goldbach's conjecture. We examine common features of other heuristics in additive prime number theory, such as Cramér's model and density-type arguments, both of which our heuristic draws from. Apart from the prime number theorem, our argument is entirely elementary, in the sense of not involving complex analysis. The idea is to model sums of two primes by a hypergeometric probability distribution, and then draw heuristic conclusions from its concentration behavior, which follows from Hoeffding-type bounds. |
| title | An elementary heuristic for Hardy-Littlewood extended Goldbach's conjecture |
| topic | Number Theory Combinatorics 11P32 |
| url | https://arxiv.org/abs/1508.05702 |