Geodesic
On a Theorem of Sylvester and Schur
Canadian mathematical bulletin, Tome 16 (1973) no. 2, pp. 195-199

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In 1892, Sylvester [7] proved that in the set of integers n, n+l,..., n+k—1, n> k > 1, there is a number containing a prime divisor greater than k. This theorem was rediscovered, in 1929, by Schur [6]. More recent results include an elementary proof by Erdös [1] and a proof of the following theorem by Faulkner [2]: Let pk be the least prime ≥2k; if n≥pk then has a prime divisor ≥pk with the exceptions and In that paper the author uses some deep results of Rosser and Schoenfeld [5] on the distribution of primes. 
Hanson, D. On a Theorem of Sylvester and Schur. Canadian mathematical bulletin, Tome 16 (1973) no. 2, pp. 195-199. doi: 10.4153/CMB-1973-035-3
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     title = {On a {Theorem} of {Sylvester} and {Schur}},
     journal = {Canadian mathematical bulletin},
     pages = {195--199},
     year = {1973},
     volume = {16},
     number = {2},
     doi = {10.4153/CMB-1973-035-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-035-3/}
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