ON A BINOMIAL COEFFICIENT AND A PRODUCT OF PRIME NUMBERS.

Let pn be the n-th prime number. We prove the following double-inequality. For all integers k ≥ 5 we have exp[k(c0 - log log k)] ≤ (k2 k)/ p1 . p2 … pk ≤ exp[k(c1 - log log k)] with the best possible constants c0 = 1/5 log 23 + log log 5 = 1.10298 … and c1 =1/192 log ( 36864 192) + log log 192 - 1/192 log (p1 . p2 … p192) = 2.04287 …. This refines a result published by Gupta and Khare in 1977. [ABSTRACT FROM AUTHOR]