Prime number of Chen

A Prime number p is called a prime number of Chen if p + 2 is a prime number or a number Semi-first. (i.e., if $\ Omega (p+2) \ 2$ , where $\ Omega \,$ is the Fonction great Omega). In 1966, Chen Jingrun showed that there exists an infinity of such prime numbers.

The first prime numbers of Chen are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101

Note the whole of the prime numbers super-singular is a subset of the whole of the prime numbers of Chen.

Rudolf Ondrejka discovered the magic square 3x3 according to with 9 prime numbers of Chen:

\begin{bmatrix}
 17 & 89 & 71 \ \
 113 & 59 & 5 \ \
 47 & 29 & 101
\end{bmatrix}

In October 2005 Micha Fleuren and the PremierForm E-group found the greatest prime number of Chen:

(1284991359 \ times 2^ {98305} + 1) \ times (96060285 \ times 2^ {135170} + 1) - 2 \,

with 70.301 digits.

The smallest member of a pair of Prime numbers twins is always a prime number of Chen. In 2005, the greatest prime number twin known is:

16869987339975 \ times 2^ {171960} \ pm 1 \,

;

It was found in 2005 by the Hungarian Zoltán Járai, Gabor Farkas, Timea Csajbok, Janos Kasza and Antal Járai. It has 51.779 digits.

Terence CAT and Ben Green proved in 2005 qu' there is an infinity of arithmetic progressions in the 3 terms of prime numbers of Chen.

External bonds

The First Pages
Yahoo! Groups on the prime number of Chen with 70301 digits
Ben Green, Terence CAT, Restriction theory off the Selberg sieve, with applications

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