ON THE SUM OF THE FIRST n PRIMES |
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Authors: | Cilleruelo Javier; Luca Florian |
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Institution: | Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain |
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Abstract: | In this note, we show that the set of n such that the arithmeticmean of the first n primes is an integer is of asymptotic densityzero. We use the same method to show that the set of n suchthat the sum of the first n primes is a square is also of asymptoticdensity zero. We also prove that both the arithmetic mean ofthe first n primes as well as the square root of the sum ofthe first n primes are well distributed modulo 1. |
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