Add new comment

Permalink

Unfortunately prime count with Li(x) and even R(x) Riemann zêta function make a very roughly count of prime with large counting deviation.

Here is a new table count for curious:

Table du décompte des nombres premiers avec Go(X) et les écarts de calcul par rapport à pi(x).

X Go(x) pi(x) -Go(x) @
1,E+01 3,9 0,1
1,E+02 24,6 0,4
1,E+03 167,7 0,3
1,E+04 1 228,4 0,6
1,E+05 9 592,6 -0,6
1,E+06 78 498,6 -0,6
1,E+07 664 578,1 0,9
1,E+08 5 761 454,3 0,7
1,E+09 50 847 534,5 -0,5
1,E+10 455 052 511,9 -0,9
1,E+11 4 118 054 813,4 -0,4
1,E+12 37 607 912 018,1 -0,1
1,E+13 346 065 536 838,3 0,7
1,E+14 3 204 941 750 802,4 -0,4
1,E+15 29 844 570 422 668,4 0,6
@ gaston ouellet

This generalized count is realized with ( X2^2 - X1^2) / ln( X2^2). Fanstastic.

Filtered HTML

  • Web page addresses and email addresses turn into links automatically.
  • Allowed HTML tags: <a href hreflang> <em> <strong> <cite> <code> <ul type> <ol start type> <li> <dl> <dt> <dd>
  • Lines and paragraphs break automatically.
  • Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.

  • What do chocolate and mayonnaise have in common? It's maths! Find out how in this podcast featuring engineer Valerie Pinfield.

  • Is it possible to write unique music with the limited quantity of notes and chords available? We ask musician Oli Freke!

  • How can maths help to understand the Southern Ocean, a vital component of the Earth's climate system?

  • Was the mathematical modelling projecting the course of the pandemic too pessimistic, or were the projections justified? Matt Keeling tells our colleagues from SBIDER about the COVID models that fed into public policy.

  • PhD student Daniel Kreuter tells us about his work on the BloodCounts! project, which uses maths to make optimal use of the billions of blood tests performed every year around the globe.