Geodesic
Six Primes and an Almost Prime in Four Linear Equations
Canadian journal of mathematics, Tome 50 (1998) no. 3, pp. 465-486

Voir la notice de l'article provenant de la source Cambridge University Press

There are infinitely many triplets of primes $p,\,q,\,r$ such that the arithmetic means of any two of them, $\frac{p+q}{2},\,\frac{p+r}{2},\,\frac{q+r}{2}$ are also primes. We give an asymptotic formula for the number of such triplets up to a limit. The more involved problem of asking that in addition to the above the arithmetic mean of all three of them, $\frac{p+q+r}{3}$ is also prime seems to be out of reach. We show by combining the Hardy-Littlewood method with the sieve method that there are quite a few triplets for which six of the seven entries are primes and the last is almost prime.
DOI : 10.4153/CJM-1998-025-1
Mots-clés : 11P32, 11N36 
Balog, Antal. Six Primes and an Almost Prime in Four Linear Equations. Canadian journal of mathematics, Tome 50 (1998) no. 3, pp. 465-486. doi: 10.4153/CJM-1998-025-1
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