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
