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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.