User:Rhnmcl

I have created further discussion on your improvement to the sieve of Eratosthenes. This algorithm was known to Euler in his Proof of the Euler product formula for the Riemann zeta function. If you would like to contribute to the debate see Talk:Sieve of Eratosthenes#Euler's sieve.

Thankyou for your time.

Zfishwiki (talk) 00:25, 3 April 2009 (UTC) If Euler's Sieve is as represented by Zfishwiki, it would seem to be substantially the same as the RRE sieve which I originally suggested. I haven't studied Euler's Sieve or his derivation.Essentially the way I came upon the RRE Sieve is a follows:

1/define a prime number as a positive integer, which has one , and only one factor other than one.

2/define a compound number as a positive integer, which has two or more factors other than one.

3/ so one is not compound,because it lacks two factors other than one. neither is it prime, because it lacks even one factor other than one.

4/then if we use: "#" as the set union symbol,"&" as the set intersection symbol and " ' " as the set complement symbol.Where: N is the set of positive integers,C is the set of compound numbers, P is the set of prime numbers and S2 is the set of all compound numbers having 2 as a factor etc.(this is just a sketch) let N1 be the set of positive integers, excluding one. then P = N1 & 'C and C = S2 # S3 # S4 etc; thus 'C = '{S2 # S3 # S4 etc } = {'S2 & 'S3 & 'S4 etc }; thus P = N1 & 'S2 & 'S3 & 'S4 etc.......(1)

5/ by imposing the requirement that redundant exclusions can be eliminated; the expression at (1) will successively expand to yield expressions which can be recognized as a/ The Sieve of Eratosthenes then b/ The RRE Sieve (or Euler's Sieve if you prefer).

I can email a pdf with the detailed derivation and with the proper set symbols should anyone be interested; regards RhnMcL