Abstract
Let p n be the nth prime. In this note, we show that the set of n such that \(\sum\nolimits_{i \leqslant n} {p_i } \) is a square is of asymptotic density zero.
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References
H. Halberstam and H.-E. Rickert, Sieve Methods, Academic Press, London, 1974.
’Open Problems’ http://www.math.leidenuniv.nl/~evertse/07-workshop-problems.pdf
N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences http://www.research.att.com/~njas/sequences/
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Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 301–306, July–September, 2007.
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Luca, F. On the sum of the first n primes being a square. Lith Math J 47, 243–247 (2007). https://doi.org/10.1007/s10986-007-0017-7
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DOI: https://doi.org/10.1007/s10986-007-0017-7