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>Moreover, the larger the number, the more ways exist to split it into a sum of two other numbers—let alone three. I don't think that makes sense. Every large
by gibybo 14y ago
>Moreover, the larger the number, the more ways exist to split it into a sum of two other numbers—let alone three.
I don't think that makes sense. Every large odd number has exactly 0 ways to find its sum with two primes^, so they can't have more ways than small numbers (which also have 0, of course). Perhaps he was speaking about the strong conjecture, but then there would be no point to say 'let alone three', because three is only relevant for the weak conjecture.
Am I missing something obvious, or did the author just word that sentence/paragraph poorly?
^I am pretty sure this trivially follows from the fact that two odd numbers always produce an even number.
- stryker 14y agoJust semantics. The writer presumably is considering only even numbers, for which it is generally true that you get more solutions as you increase the number. You are right in that it is worded non-rigorously, but in my opinion it is implied from the context.
- bkirwi 14y agoHe says numbers, not primes, so it's trivially correct. Though that doesn't directly imply the conjecture being true for sufficiently large numbers, since primes become increasingly sparse as one moves up the number line... it seems more like an appeal to intuition than a real argument, to me.