“Introspective arbitrage” is counting evidence twice.

Yes, as time goes by without an answer, the number is (more or less monotonically) increasingly more likely to be prime. But that’s because stopping time *depends* on your subjective likelihood of possible answers. If you then change your likelihood based on stopping time, you’re lending your self-generated “rumor” more credence than actual evidence warrants.

]]>yes you are right. if i use a stopping rule then i either find a factor before the stopping time or i don’t and then i guess prime at the stopping time. i don’t know what i was thinking.

]]>Sure, but this process still leads to composite guesses taking a shorter amount of time than prime guesses?

]]>I was wondering the same.

-Conclude 2 is prime, quickly make ++$5.00

-Conclude 3 is prime, quickly make ++$3.20

-Conclude 5 is prime, quickly make ++$0.70

…

[She doesn’t have to do these calculations of how much money each sieve operation makes.]

I guess the main downside is that she has to either (i) redundantly say numbers more than once, or (ii) remember which numbers she’s said.

]]>You then may want to exhaust “squares” (49, 81) and any other rule you know, like how to rule out composites of 3.

At the end, if you still have time, you will have to check odd numbers, not ending on 5, not multiples of 3, in the interval 60-100… and that will take a lot of time, for each number… ]]>

I don’t think that’s how we look for factors. At least it’s not how I do. It’s more of a passive thing where factors suggest themselves. When I say 49 you don’t check 2 then 3 then 4… Instead the number 7 just jumps into your head. If you wait long enough and no factor has jumped into your head then you guess prime.

]]>