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## my best prime generation function yet! [Fwd: SEQ FROM Roger L. Bagula]

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• With a functional Shannon entropy power of N=1/log(n) this function misses the first three primes , but does very well in the lower primes after that.
Message 1 of 1 , Jan 31, 2004
With a functional Shannon entropy power of N=1/log(n)
this function misses the first three primes ,
but does very well in the lower primes after that.
Derivation goes like this from Shannon's formula
for the entropy power of white noise:
N1=(1/2*Pi*E)*Exp(2*H)
when ( linear transform of n to Prime[n] )
H=Log(Prime[n]/n)
then
N1=(E/(2*Pi))*Prime[n]/n
or
Prime[n]=2*Pi*n*N/E
and the asymptotic prime distribution function is:
PrimePi[n]--> n/Log(n)
which gives
N=1/Log(n)
as used here.

-------- Original Message --------
Subject: SEQ FROM Roger L. Bagula
Date: Sat, 31 Jan 2004 16:23:44 -0500 (EST)
From: <njas@...>
To: njas@...
CC: tftn@...

The following is a copy of the email message that was sent to njas
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Subject: NEW SEQUENCE FROM Roger L. Bagula

%I A000001
%S A000001 7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,
109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,
223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,
331
%N A000001 An entropy power of white noise function with N=1/log(n)
%C A000001 Function is based on asymptotic form of distribution:
PrimePi[n]--> n/log(n)
Function misses the first three primes {2,3,5} , but is pretty good after that.
%D A000001 Claude E. Shannon, The Mathematical Theory of Communications, page 63
%F A000001 a(n) = if Floor[2*Pi*n/(E*Log[n])] is prime then Floor[2*Pi*n/(E*Log[m])]
%t A000001 digits=5*200
f[n_]=Floor[2*Pi*n/(E*Log[n])]
a=Delete[Union[Table[If [PrimeQ[f[n]]==True,f[n],0],{n,2,digits}]],1]
%O A000001 2
%K A000001 ,nonn,
%A A000001 Roger L. Bagula (tftn@...), Jan 31 2004
RH
RA 209.179.51.13
RU
RI

--
Respectfully, Roger L. Bagula
tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :