Sum of Squares of Consecutive Primes using Maximal Gap

A.Gnanam; M.A.Gopalan; B.Anitha

doi:https://doi.org/10.14445/22315373/IJMTT-V19P514

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 19 | Number 2 | Year 2015 | Article Id. IJMTT-V19P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V19P514

Sum of Squares of Consecutive Primes using Maximal Gap

A.Gnanam, M.A.Gopalan, B.Anitha

Citation :

A.Gnanam, M.A.Gopalan, B.Anitha, "Sum of Squares of Consecutive Primes using Maximal Gap," International Journal of Mathematics Trends and Technology (IJMTT), vol. 19, no. 2, pp. 108-111, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V19P514

Abstract

In this paper an attempt has been made to find the sum of squares of consecutive primes using G(x), familiarly known as the maximal gap between consecutive primes. Here conjectures of [1,2] namely G(x)∼logx(logx-2loglogx+C), G(x)∼(logx)^2, G(x)∼logx(logx+logloglogx) have been considered. Relations among values of x and the gaps between consecutive primes are presented here. The results are analyzed for the primes ≤〖10〗6and to a gap of 72.

Keywords

Maximal gaps between primes, Polygonal numbers.

References

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