Conjectures on Representations Involving Primes

@article{Sun2015ConjecturesOR,
  title={Conjectures on Representations Involving Primes},
  author={Z. Sun},
  journal={arXiv: Number Theory},
  year={2015},
  pages={279-310}
}
  • Z. Sun
  • Published 2015
  • Mathematics
  • arXiv: Number Theory
  • We pose 100 new conjectures on representations involving primes or related things, which might interest number theorists and stimulate further research. Below are five typical examples: (i) For any positive integer n, there exists \(k\in \{0,\ldots ,n\}\) such that \(n+k\) and \(n+k^2\) are both prime. (ii) Each integer \(n>1\) can be written as \(x+y\) with \(x,y\in \{1,2,3,\ldots \}\) such that \(x+ny\) and \(x^2+ny^2\) are both prime. (iii) For any rational number \(r>0\), there are distinct… CONTINUE READING
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