[schoen]

I've unfortunately received somewhere around 100 supposed formulas for primes in the past decade and a half. :-(

There's a great Wikipedia article about this:

https://en.wikipedia.org/wiki/Formula_for_primes

But most of what people send me is along the lines of "numbers containing only odd digits, that don't end in 5" or "4k+1 for any k, if it contains only odd digits", or "(p-1)²+7 for any prime p" or whatever. A kind of unfortunate example was an elementary school girl who became convinced that numbers containing only odd digits are always prime (many people are tempted by some form of this idea), and spent several weeks writing such digits down in a composition notebook in order to form an integer that would be big enough to qualify for one of our awards.

[pklausler]

And the counterexample of 15 didn't work?

[schoen]

I've come up with counterexamples for every such formula or rule that people have sent me (usually running a Python loop with gmpy2.is_prime() or something), but unfortunately the existence of the counterexamples somehow didn't occur to them before they wrote in in the first place.

https://en.wikipedia.org/wiki/Mathematical_coincidence is a big problem because people will sometimes conjecture a pattern and then find that it holds for 6 or 7 integers and conclude that it's right. Or if they find a counterexample, they might just make a minimal modification to the conjecture and conclude that they're fixed it! So there are lots of these that will say "unless the number is..." and presumably give some other random property that the counterexample that the claimant found had.

It feels like some people think that mathematics works by people guessing rules and then checking them, and regarding the rules as right if they "check out" in practice. (I know that there's been lots of progress made from guesses and conjectures and numerical experiments; the issue is just what comes after the guess!)

[senorprogrammer]

> mathematics works by people guessing rules and then checking them

This will sound facetious, but I suspect many people treat great swathes of life this way. My wife has a friend who tries any random googled herb-based cure any time she gets ill. Recovery from this illness, this cold or flu, is always taken as proof of the validity of the cure, regardless of how long she's had to ingest it.

You, reading this, have already thought of half a dozen ways to disprove her cures, as have I, however no amount of evidence can assuage this need to believe. At this point my theory is that this belief forms an intractable part of her personal identity.

At the core of all of this, and perhaps for these "autodidact physicists" as well, seems to be a very primal need to understand the universe in terms comprehendible one's self, regardless the cost.

[ktRolster]

> mathematics works by people guessing rules and then checking them

This will sound facetious, but I suspect many people treat great swathes of life this way

Including programming. Good programmers are the ones who try to derive the underlying rules, instead of trying something and checking if it works for a couple cases.

[duaneb]

Or 9.

[pklausler]

Ah. I took "digits" to mean "must be plural", not "could be".