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
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