On Thu, Aug 23, 2018 at 08:47:12AM -0700, Brent Meeker wrote: > > > On 8/22/2018 7:01 PM, Jason Resch wrote: > > There are also programs for which no one knows if they are computable or > > not. If you can prove whether or not this function ever completes, you > > will be world famous, and may even earn a million dollars (though I > > think the prize has been retracted, it might be oferred again): > > > > Step 1: Set X = 4 > > Step 2: Set R = 0 > > Step 3: For each Y from 1 to X, if both Y and (X – Y) are prime, set R = 1 > > Step 4: If R = 1, Set X = X + 2 and go to Step 2 > > Step 5: If R = 0, print X and halt > > > > All you have to prove is the computer either never gets to step 5 or > > that it does get to step 5. Mathematicians have been working on a > > related problem for 300 years, no one has solved it yet. > > X=6 so go to Step 2 and Set R=0 > When Y=2 and (X-Y)=4 they are not both prime. Leave R=0. > Go to step 5 print 6 and halt.
I read step 3 as a loop, ie check all Y from 1 to X (actually 1 to X/2 will suffice) before moving to step 4. In your example, the loop will check Y=3, and (X-Y)=3, so R=1, and so step 4 mean X=X+2 and step 2 is executed again. IIUC, if the twin primes conjecture were true, then the above program will never halt, but I could be wrong on that. Cheers -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow hpco...@hpcoders.com.au Economics, Kingston University http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
