International Journal of Mathematics Trends and Technology
Volume 19 | Number 2 | Year 2015 | Article Id. IJMTT-V19P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V19P514
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.
[1] H. Cramer. On the order of magnitude of difference between consecutive prime numbers. Acta Arith., II:23–46, 1937.
[2] D. R. Heath-Brown. Differences between consecutive primes. Jahresber. Deutsch. Math.-Verein, 90:71–89, 1988.
[3] J.Y.Liu., On Lagrange’s theorem with prime variables,Quart.J.Math. (Oxford) 54 (2003) 454-462.
[4] J.Y.Liu.,G.S.Lu,T.Zhan, Exponential sums over primes in short intervals,Sci.China Ser.A 36(2006)448- 457.
[5] J.Y.Liu, T.Zhan, On sums of five almost equal prime squares, Acta Arith. 77 (1996) 369-383.
[6] X.M.Meng,On sums of a prime and four squares in short intervals,Acta Math.Hungar,105 (2004) 261-283.
[7] G. Harman, A.V. Kumchev, On sums of squares of primes, Math. Proc. Cambridge Philos. Soc. 140 (2006)1–13.
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
PDF 
Abstract 
Keywords 
References 
Citation