Geodesic
Generalizing a theorem of Schur
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 1063-1065.

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In a letter written to Landau in 1935, Schur stated that for any integer $t>2$, there are primes $p_{1}$ such that $p_{1}+p_{2}>p_{t}$. In this note, we use the Prime Number Theorem and extend Schur's result to show that for any integers $t\ge k \ge 1$ and real $\epsilon >0$, there exist primes $p_{1}$ such that \[ p_{1}+p_{2}+\cdots +p_{k}>(k-\epsilon )p_{t}. \]
DOI : 10.1007/s10587-014-0153-2
Classification : 11A41, 11N05
Keywords: Prime Number Theorem; Schur 
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Jones, Lenny. Generalizing a theorem of Schur. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 1063-1065. doi : 10.1007/s10587-014-0153-2. http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0153-2/

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