[Jprogramming] Testing consecutive pairs of primes

[greg heil]

Wm

Saith William Tanksley, Jr <wtanksleyjr at gmail.com>:
>>something that other posters have explained in the past

>Indeed i was one of those who said, in this thread, that. So i am in complete concurrence on this. To answer, constructively, Alan's post i made the new hypothesis which was perhaps more sensible given the clear typos in the text.

Saith William Tanksley, Jr <wtanksleyjr at gmail.com>:
>>2 is not equal to (3+5)%2

>Indeed, but it is equal to (3+5)%4, as my hypothesis asks of it.

Saith William Tanksley, Jr <wtanksleyjr at gmail.com>:
>> 2,3 is "a pair of primes"

>Not in the sense i used, and i think is commonly used, where the pairs are separated by two. There are as many adjacent primes as there are primes. So to make prime pairs meaningful, one has to put a restriction on them.

Saith William Tanksley, Jr <wtanksleyjr at gmail.com>:
>>I got the impression that everyone here was talking about the average of two primes, not half of the average.

>Exactly i interpreted a NEW hypothesis from an obviously typo 'd one. That was the original motivation. Alan stated that he would like to see algorithmic explorations for his hypothesis ... which was clearly typo 'd. So i made one: a correctly stated related hypothesis and an algorithmic exploration.

>Certainly my hypothesis holds for all reasonably computable primes. i would be curious if it holds also generally.

greg
~krsnadas.org

--

from: William Tanksley, Jr <wtanksleyjr at gmail.com>
to: programming at jsoftware.com
date: 14 May 2013 07:37
subject: Re: [Jprogramming] Testing consecutive pairs of primes

greg heil <gheil.j at gmail.com> wrote:
> 2.5 is not even an integer, how could it be a prime?

>The confusion for me is probably the same as for Raul. You are making statements like "the hypothesis is true for all numbers tested except 2 and 3." This is confusing to both Raul and myself, because the statement of the hypothesis we're thinking of is false by definition (something that other posters have explained in the past); you are obviously thinking of some other hypothesis that somehow isn't false.

>The hypothesis we're considering is the claim that there exists a prime number that is equal to the average of the primes in a paired prime. The hypothesis that you're considering is something I'd never seen before -- you stated it below.

>>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.

>2 is not equal to (3+5)%2, nor is 3 equal to (5+7)%2. So those are not solutions according to the original statement. I don't know what they're solutions to -- I suspect they're the result of a bug.

>The first paired primes are 3,5, and their average is 4. 2,3 is "a pair of primes", and the only adjacent primes; their average is 2.5.

>>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.

>Well... I for one am deeply surprised to see the '4' there. I'll be glad to feel stupid if you'll point out where that '4' was explained... I got the impression that everyone here was talking about the average of two primes, not half of the average.

>I'll try to think about your question, which certainly has the advantage of not being obviously false, unlike the question Raul and I thought you were asking. In the meantime, could you discuss your actual question a little more -- what motivated it?

-Wm