login
A semi-empirical prime like function with primes isolated.
0

%I #8 Dec 18 2022 06:08:08

%S 3,5,11,79,109,131,211,223,229,241,271,277,347,353,379,443,463,509,

%T 523,557,571,577,631,727,827,877,971,1051,1103,1229,1237,1259,1303,

%U 1409,1439,1447,1493,1531,1669,1723,1747,1801,1847,1871,1979,1987,2081,2089

%N A semi-empirical prime like function with primes isolated.

%t (*first entropy constant to n=10000*)

%t p0[n_]=PrimePi[n]/n

%t a=Table[ -p0[n]*Log[p0[n]], {n, 2, 10000}];

%t w0=N[Apply[Plus, a], 200]/10000

%t (*Second entropy constant to n=10000*)

%t z0=Sum[PrimePi[n]/(n*Prime[n]), {n, 1, 10000}];

%t (* semi-empirical prime-like function based on prime entropy sums*)

%t p[n_]=Sum[ -Log[PrimePi[i]/i], {i, 2, n}]

%t a0=Table[If[PrimeQ[Floor[p[n]*(2+E+z0/n+w0)]]==True, Floor[p[n]*(2+E+z0/n+w0)], 0], {n, 2, 1000}];

%t c0=Delete[Union[a0], 1]

%K nonn,uned,obsc,less

%O 2,1

%A _Roger L. Bagula_, Dec 03 2003