Life In 19x19

primes = #@!?b + primes - #@!?b

the interesting idendities are the ones with different left and right sides.

Bill Spight wrote:
What is the simplest formula that works?

This is argument which is backing up your claim? I must admit, i expected sth much better.

AloneAgainstAll: your formula is correct, but doesn't do the job that one would expect from a formula. This conversation is a bit like:

- Go Master: assuming komi is (fair komi + 0.5), there is no known method to win a go game as white 100% of the time.

- StudentAloneAgainstAll: I disagree. You can explore the entire tree and search for an optimal path.

You really think this is good paraphrase? I dont think so. There are things we cant "enclose" in mathemathical formulas (like results of integral of sin(x^2) cant be described by elementary functions, only infinite sum ) etc. So the fact that we can produce such a formula (even if its completely useless for computing) is mathemathically significant.

What is significant and what is not is a matter of personal taste. So let's agree that we disagree here...

But you agree that there is significant difference between:

1.There is no formula
2.There is no formula usefull for computing.

We werent talking about 2nd at all! If you want, we can talk about usefull formulas for computing prime numbers in completely different thread, but lets keep this talk about what it was.


To not derail original thread completely, i want to say that i feel jealous for ppl who believe that bad teachers does not exist - they must have met only good teachers in their whole like, which is very good for them.

I agree that bad teachers exist, however it is not easy to determine if someone is a good or a bad teacher. Certainly someone who teaches wrong ideas/mistakes, or who breaks student's motivation, is a bad teacher, but outside extreme cases like that, I think that the student's progress has much more to do with his passion and with a stimulating environment (competition against other students) than with the teaching abilities of the master.

AloneAgainstAll wrote:You really think this is good paraphrase? I dont think so. There are things we cant "enclose" in mathemathical formulas (like results of integral of sin(x^2) cant be described by elementary functions, only infinite sum ) etc. So the fact that we can produce such a formula (even if its completely useless for computing) is mathemathically significant.

Ok, I define S(t) as the integral of sin(x^2) from 0 to t. Now I can write you a nice short correct formula for it, i.e. S(t). Yes, it does not use elementary functions only, but your prime formula with floor functions does not use only elementary functions either. The whole issue is really about what kind of formulas we allow.

I don't dispute that maybe you had a bad teachers, and maybe he/she could have discussed the nuances of formulas and algorithms better.