Changes

In 1966, Chen Jingrun showed that there are infinitely many [[prime]]s p such that p+2 is either a [[prime]] or the product of two [[prime]]s (a "[[semiprime]]"), relying on a sieve theory.  This resulted in defining a "Chen prime" to be a prime p such that p+2 is either a prime or a [[semiprime]].  In 2005, Ben Green and Terence Tao proved that there are [[infinite]]ly many three-term arithmetic progressions of Chen primes.

In 1966, Chen Jingrun showed that there are infinitely many [[prime]]s p such that p+2 is either a [[prime]] or the product of two [[prime]]s (a "[[semiprime]]"), relying on a sieve theory.  This resulted in defining a "Chen prime" to be a prime p such that p+2 is either a prime or a [[semiprime]].  In 2005, Ben Green and Terence Tao proved that there are [[infinite]]ly many three-term arithmetic progressions of Chen primes.

In 1915, [[Viggo Brun]] proved that the sum of reciprocals of the [[twin primes]] is convergent.  This sum converges on [[Brun's constant]].

In 1915, [[Viggo Brun]] proved that the sum of reciprocals of the [[twin primes]] is convergent.  This sum converges to [[Brun's constant]].

== Sources ==

== Sources ==

*[http://mathworld.wolfram.com/TwinPrimeConjecture.html Math World]

*[http://mathworld.wolfram.com/TwinPrimeConjecture.html Math World]

[[Category:Number Theory]]

[[Category:Prime Numbers]]