Re: next Prime method from sci.math post

*To*: mathgroup at smc.vnet.net*Subject*: [mg52192] Re: [mg52168] next Prime method from sci.math post*From*: DrBob <drbob at bigfoot.com>*Date*: Sun, 14 Nov 2004 04:30:48 -0500 (EST)*References*: <200411130940.EAA01018@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

Roger, The range of your f function includes most integers (10000 of the first 10042, for instance): Clear[f] digits = 10000; f[n_] := Floor[n + Log[n]^2/2] z=f/@Range@digits; Length@z Through[{Min,Max}@z] 10000 {1,10042} ...so OF COURSE the range includes most primes. That is, most primes are f[n] for some n. (Using the word "most" very loosely.) But here's an f function that doesn't miss any at all!!! Clear[f] digits=10000; f[n_]:=n a=Rest@Union@Table[If[PrimeQ@f@n,f[n],0],{n,1,digits}]; b=Prime@Range@Length@a; Complement[b,a] {} All primes fit that pattern, so I'm thinking of naming it the "Treat-Bagula prime finder function". What do you think? Bobby On Sat, 13 Nov 2004 04:40:19 -0500 (EST), Roger Bagula <tftn at earthlink.net> wrote: > I read a post several days ago that said you could find a prime between > n and n+Log[n]^2. > ( there also seems to be a NextPrime[] function in Mathematica that I > wasn't aware of) > I tried the average of the two and it works very well > such that there are only a few primes that don't fit that pattern: > > (* Primes that aren't at the average of n and n+Log[n]^2 *) > Clear[f] > digits=10000 > f[n_]:=Floor[n+Log[n]^2/2] > a=Delete[Union[Table[If[PrimeQ[f[n]]==True,f[n],0],{n,1,digits}]],1]; > b=Table[Prime[n],{n,1,Dimensions[a][[1]]}]; > Complement[b,a] > {5,37,97,421,673,2659,3407,3847,7703} > Respectfully, Roger L. Bagula > > tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 : > alternative email: rlbtftn at netscape.net > URL : http://home.earthlink.net/~tftn > > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**next Prime method from sci.math post***From:*Roger Bagula <tftn@earthlink.net>