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
7 Citations