Somewhat off topic: Greg, I find reading your posts here quite confusing as you seem to use a leading ">" (typically indicating quoted text) as a bullet. It's possible that some folks are skimming over these paragraphs accidentally.
Best, M On Tue, May 14, 2013 at 3:08 PM, greg heil <[email protected]> wrote: > Raul > > >?? Where did that come from? As to the congruity of subjects we are > speaking of ... that is truly a philosophical question which, unlike > Wittgenstein, is a morass i would prefer not to indulge in. Your > contributions have beenvery, nay extremely, valuable to me over the years > and so i will try to make this comment as just such a learning experience. > > > 2.5 is not even an integer, how could it be a prime? i am just as prone > to typos as anyone. (i do have a spell checker but it cannot reach all!) > Indeed in this thread i typed 5 when i meant 4. However i never recall > intimating that 2.5 was a prime. Nor on review can i see that... > > >In your quote i said that 2 and 3 were the only solutions (note the > plural) up to 1e8, of hpp. 2 is the solution for the prime pair (pp) 3 5, > while 3 is for 5 7. > > >Maybe i will be very happy to know of my stupidity for not seeing a > yeoman's proof that my hypothesis were true (that there are no r -: 4%~p+q > where p, q, and r are primes and p q is a prime pair) except for the > trivial pairs of 3 5 and 5 7. > > >i should be very happy to receive such a proof, or improvements to any of > my functions. i can learn from such input. > > >Let me repeat the functions i used in my numerical experiment: > > ps=: p:@i. NB. primes > pp=: ((2&+) = (1&|.)) NB. prime pair? > pq=:1&p: NB. prime? > pip=:(>@{:) @(pp </. ])@ps > hpp=: >@}:@(pq ek ]) @ (-:@>:@pip) NB. half primes of pairs > > hpp 1e8 > 2 3 > > greg > ~krsnadas.org > > -- > > from: Raul Miller <[email protected]> > to: Programming forum <[email protected]> > date: 14 May 2013 04:42 > subject: Re: [Jprogramming] Testing consecutive pairs of primes > > On Mon, May 13, 2013 at 8:58 PM, greg heil <[email protected]> wrote: > > i suppose your point might be true in some abstract sense. hpp shows > > that for all practically computable primes the hypothesis is true, > > except for the primes of 2 and 3. > > Are you saying 2.5 is a prime number? > > Or are we talking about different subjects? > > -- > > from: greg heil <[email protected]> > to: Programming forum <[email protected]> > date: 13 May 2013 17:58 > subject: Re: [Jprogramming] Testing consecutive pairs of primes > > Raul > > >i suppose your point might be true in some abstract sense. hpp shows that > for all practically computable primes the hypothesis is true, except for > the primes of 2 and 3. In any case Alan asked for examples of _software_ > which would address such issues by testing examples. This is a response to > that, not something he defined, explicitly, as not an issue. > > greg > ~krsnadas.org > > -- > > from: Raul Miller <[email protected]> > to: Programming forum <[email protected]> > date: 13 May 2013 10:25 > subject: Re: [Jprogramming] Testing consecutive pairs of primes > > >Induction, by inspection of a prefix of the sequence of prime numbers, is > not very satisfying because prime numbers are not uniformly distributed. > > >For a prefix to be relevant, we have to have reason to believe that the > rule is applied uniformly, beyond that prefix, despite any varied > distribution. > > >Henry's proof did not need induction on prime numbers because he was > relying on properties of numbers (which we have reason to believe are > uniformly distributed). > > >Put differently, the "induction" used here did not show how "the proof > about prime numbers pairs beyond the tested prime pairs" were related to > "the proof about prime number pairs within the tested prime pairs". That's > akin to saying "10 is the next digit after 9" even though 10 is not a digit. > > -- > > from: greg heil <[email protected]> > to: Programming forum <[email protected]> > date: 13 May 2013 09:46 > subject: Re: [Jprogramming] Testing consecutive pairs of primes > > >2 and 3 are the only results of hpp 1e8 so pseudo induction seems to be > very consistent here. Are there any other primes of the form 4%~p+q where p > and q are paired primes? Maybe there is logic to say it is so. Or maybe a > better algorithm can extend well beyond 1e8... > > greg > ~krsnadas.org > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
