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Partitions of primes and other sequences

Published online by Cambridge University Press:  01 August 2016

K. Robin McLean
K. Robin McLean*
Affiliation:
Dept of Education, University of Liverpool, PO Box 147, Liverpool L69 3BX
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Let p 1, p 2, p 3, … be the sequence of primes. Take any integer n ⩾ 2 and partition the set {p 1p 2, … , p n} into two non-empty subsets A and B. Let P A be the product of primes in A and P B be the product of primes in B. No partition exists with P A = P B, because of the uniqueness of prime factorisation, but Fernando Castro’s neat result in [1] asserts that for each n there is a partition for which 1

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Articles
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The Mathematical Gazette , Volume 89 , Issue 514 , March 2005 , pp. 15 - 21
Copyright
Copyright © The Mathematical Association 2005

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References

1. Fernando Castro, G., More on the sequence of prime numbers, Math. Gaz. 86 (July 2002) pp. 264–265.Google Scholar
2. Ribenboim, P., The book of prime number records, Springer-Verlag (1988).Google Scholar
3. Hardy, G.H., A course of pure mathematics (10th edn.), Cambridge University Press (1952).Google Scholar