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

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

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(3.37)n, and Selfridge (unpublished) proved A(n)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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[1] 1. Appel, K. I. and Rosser, J. B., Tables for estimating functions of primes, Comm. Research Div. Technical No. 4, Von Neumann Hall, Princeton, N.J. (Sept. 1961). Google Scholar

[2] 2. Hardy, G. H. and Wright, E. M., The theory of numbers, Oxford Univ. Press, London, Ch. XXII, 4th éd., 1959. Google Scholar

[3] 3. Moser, L., On the product of the primes not exceeding n , Canad. Math. Bull. (2) 2 (1959), 119-121. Google Scholar

[4] 4. Rosser, J. B. and Schoenfeld, L., Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94. Google Scholar

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