Chen prime
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A prime number p is called a Chen prime if p + 2 is either a prime or a semiprime. It was in 1966 that Chen Jingrun proved that there are infinitely many such primes.
The first few Chen primes are
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101 (sequence in OEIS)
Note that all of the supersingular primes are Chen primes.
Rudolf Ondrejka discovered the following 3x3 magic square of nine Chen primes:
| 17 | 89 | 71 |
| 113 | 59 | 5 |
| 47 | 29 | 101 |
In October 2005 Micha Fleuren and PrimeForm e-group found the largest known Chen prime, (1284991359 · 298305 + 1) · (96060285 · 2135170 + 1) − 2 with 70301 digits.
The lower member of a pair of twin primes is always a Chen prime. As of 2005, the largest known twin prime is 16869987339975 · 2171960 ± 1; it was found in 2005 by the Hungarians Zoltán Járai, Gabor Farkas, Timea Csajbok, Janos Kasza and Antal Járai. It has 51779 digits.
Terence Tao and Ben Green proved in 2005 that there are infinitely many three-term arithmetic progressions of Chen primes.
External links
- [The Prime Pages]
- [Yahoo! Groups message about Chen prime with 70301 digits]
- Ben Green, Terence Tao, [Restriction theory of the Selberg sieve, with applications]
- , [Chen Prime] at MathWorld.
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