An elementary formula to know the number of primes in the interval (x, 2x) close to the exact figure for a fixed x is given here. A new elementary equation is derived (a relation between prime numbers and composite numbers distributed in the interval [1, 2x]). An elementary method to know the number of primes in a given magnitude is suitably placed in the form of a general formula, and we have proved it. The general formula is applied to the terms of the equation, and a tactical simplification of the terms gives rise to an expression whose verification envisages scope for its further studies.
References
[1]
Hardy, G.H. and Wright, E.M. (2007) An Introduction to The Theory of Numbers. Academic Press, Oxford.
[2]
Erdös, P. (1932) Beweis eines satzes von tschebyschef. Acta Scientiarum Mathematicarum, 5, 194-198.
[3]
Ramanajun, S. (1919) A Proof of Bertand’s Postulate. The Journal of the Indian Mathematical Society, 11, 181-182.
[4]
Meissel, E.D.F. (1870) Uebr die Bestimmung der Primzahlenmenge innerhalb gegebener Grenzen. Mathematische Annalen, 2, 636-642. https://doi.org/10.1007/BF01444045
[5]
Meissel, E.D.F. (1871) Berechnung der Menge von Primzahlemahlen, welche innerhalb der ersten Hundert Millionen natürlicher Zahlen vorkommen. Mathematische Annalen, 3, 523-525. https://doi.org/10.1007/BF01442832
Meissel, E.D.F. (1885) Berechnung der Menge von Primzahlemahlen, welche innerhalb der ersten Milliarde natlurlicher Zahlen vorkommen. Mathematische Annalen, 25, 251-257. https://doi.org/10.1007/BF01446409
[8]
Lehmer, D.H. (1958) On The Exact Number Of Primes Less Than A Given Limit. Illinois Journal of Mathematics, 3, 381-388. https://doi.org/10.1215/ijm/1255455259
[9]
Legendre. (1808) Theorie des nombress. 2nd Edition, Chez Courcier, Paris, 420.
[10]
Caldwell Chris, K. (1982) A Table of Values of . A Website by Caldwell Chris. https://primes.utm.edu
