Name of a conjecture on difference of prime numbers? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-23T23:33:13Z http://mathoverflow.net/feeds/question/111196 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/111196/name-of-a-conjecture-on-difference-of-prime-numbers Name of a conjecture on difference of prime numbers? ali 2012-11-01T19:29:13Z 2012-11-01T20:42:49Z <p>Hello Dear</p> <p>there is a conjecture for which I do not know how it is called. The conjecture is:</p> <blockquote> <p>Every even number can be always written as the difference between two prime numbers.</p> </blockquote> <p>Could you please help me to know how it is called?</p> <p>Regards,</p> http://mathoverflow.net/questions/111196/name-of-a-conjecture-on-difference-of-prime-numbers/111208#111208 Answer by quid for Name of a conjecture on difference of prime numbers? quid 2012-11-01T20:29:33Z 2012-11-01T20:29:33Z <p>The specific conjecture that every even number is the difference of two primes appears to be due to Maillet (1905) as per <a href="http://arxiv.org/pdf/1206.0149.pdf" rel="nofollow">the paper mentioned in comments</a>. </p> <p>However, I have never heard this name before. What is a quite common name, also mentioned in comments but perhaps somewhat misleadingly, for something <em>related</em> (but stronger) is <a href="http://en.wikipedia.org/wiki/Polignac%27s_conjecture" rel="nofollow">de Polignac's conjecture</a> stating that every even number is the difference of <em>infinitely many</em> pairs of <em>consecutive</em> primes. This conjecture is also older (1849), which might explain why the more recent weaker one is not so commonly known. </p> <p>In addition, also from the mentioned paper, Kronecker (1901) made the conjecture that every even number is the difference of infinitely many pairs of primes (so stronger than Maillet but weaker than de Polignac). </p> <p>Finally, a still stronger conjecture would be the (first) Hardy-Littlewood conjecture. </p>