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the actual examples I give are just that, examples. why not numbers that can only be produced as the sum of 17 primes? or 459? or numbers that have the same num
by permo-w 3y ago
the actual examples I give are just that, examples. why not numbers that can only be produced as the sum of 17 primes? or 459? or numbers that have the same number of factors as their digits added together does? there are infinite of these constraints that can be invented. why is this one particularly interesting
- naikrovek 3y agoI can't tell if you're really asking, so I'll answer as if you are: learning these things brings greater understanding and greater understanding brings advances in multiple fields. the most fundamental questions are going to be answered (or at least conceived of and worked on) first. answering the most fundamental questions often brings the largest leaps in understanding as well, which is why untouchable numbers are considered more notable than "numbers which can be expressed as the sum of 17 primes", and so on.
- lozenge 3y agoAll the examples you gave before have already been studied and are also particularly interesting. Maths is a huge and well explored field.
- earthboundkid 3y agoBecause Platonism is true and math is a telescope that lets us glimpse at the world of ideals.
- erehweb 3y agoAs an attempt - it's a simple definition, easy to check for small numbers, but leads to some difficult questions - are there infinitely many of them? (found yes by Erdos) How dense are they in the number line? Are there any odd ones > 5? "Numbers that can only be produces as the sum of 459 primes" is not as easy to find examples of, so less aesthetically pleasing to mathematicians.
- romusha 3y agoBecause dees n