On Mon, May 13, 2013 at 12:46 PM, greg heil <[email protected]> wrote: >>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 5%~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...
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. -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
