Geodesic
On the Product of the Primes
Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 33-37

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In recent years several attempts have been made to obtain estimates for the product of the primes less than or equal to a given integer n. Denote by the above-mentioned product and define as usual Analysis of binomial and multinomial coefficients has led to results such as A(n)<4n, due to Erdôs and Kalmar (see [2]). A note by Moser [3] gave an inductive proof of A(n)<(3.37)n, and Selfridge (unpublished) proved A(n)<(3.05)n More accurate results are known, in particular those in a paper of Rosser and Schoenfeld [4] in which they prove Θ(n)< 1.01624n; however their methods are considerably deeper and involve the theory of a complex variable as well as heavy computations. Using only elementary methods we will prove the following theorem, which improves the results of [2] and [3] considerably. 
Hanson, Denis. On the Product of the Primes. Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 33-37. doi: 10.4153/CMB-1972-007-7
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