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Teenager solves stubborn riddle about prime number look-alikes

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Re: Teenager solves stubborn riddle about prime number look-alikes

#241

Post by Manu40 »

saberience wrote: post #213
Manu40 wrote: post #188

Earlier quoted context omitted.

You are so far from wrong, it hurts me to think about it. Due to having a reading level 10 years ahead of my peers, and already having learned math concepts at least 4 years ahead of them... at age 8... I was put 3 years ahead of my peers in school until the teachers realized the other kids were having none of it. They put me back in the 'proper' grade, because 'I' somehow wasn't going to develop social skills well e…

I was horribly bullied for being more advanced than my same-age classmates AND older children at high-school, placing me with even older kids (with whom presumably I would have even less in common) doesn't seem like it would have helped my situation.

Yeah, no... it probably wouldn't have helped; very much so for the reasons I have stated in reply to Tambourine.

That said, I should add that 2 of those students ended up running into me again years later. They apologized, which was nice; but then offered me the chance to go do lines of coke with them...

I declined, and went on with my life knowing doubly that my instinct about them was correct the whole time. Wastes of skin.

Re: Teenager solves stubborn riddle about prime number look-alikes

#242

Post by gnubison »

vitus wrote: post #129
renewiltord wrote: post #22

Summary: 1. Fermat's Little Theorem: if p is prime, then b^p = b (mod p) for all integers b. i.e. b^p - b is always a multiple of p. 8^3-8 = 512-8 = 504 = 168 x 3. 2. Is the inverse true? Does b^n - b = 0 (mod n) mean that n is prime? No. Sometimes n is non-prime (like n=561, divisible by 3). We call these n, Carmichael numbers. 3. Okay, so these numbers exist. How common are they? For primes we know they're common.…

> It ain't as pretty as just between straight integer multiples, but the fact that it exists in some shape at all is cool! Actually: the form that Larsen proved is stronger than "for sufficiently large X, there is at least one Carmichael number between X and 2X". So with the more specific proof, he also proved the simpler statement that's easier to express.

What is the stronger version?

Re: Teenager solves stubborn riddle about prime number look-alikes

#243

Post by renewiltord »

gnubison wrote: post #242
vitus wrote: post #129

Earlier quoted context omitted.

> It ain't as pretty as just between straight integer multiples, but the fact that it exists in some shape at all is cool! Actually: the form that Larsen proved is stronger than "for sufficiently large X, there is at least one Carmichael number between X and 2X". So with the more specific proof, he also proved the simpler statement that's easier to express.

What is the stronger version?

Bertrand's postulate is that there is at least one prime between x and 2x for x>=1

Daniel Larsen's result here is that there are e^((log x)/((log log x)^(2+d))) Carmichael numbers between x and (x + x/((log x)^(1/(2+d)))) for x>=X (depends on d)

e^((log x)/((log log x)^(2+d))) is >= 1 for all x >= 1.

(x + x/((log x)^(1/(2+d)))) Stronger by being tighter than the (x,2x) bound and being more specific about the >= 1 number of Carmichael numbers

Re: Teenager solves stubborn riddle about prime number look-alikes

#244

Post by pedrosorio »

TimTheTinker wrote: post #236
pedrosorio wrote: post #226

Earlier quoted context omitted.

Which would be useless in context because even for quadratic polynomial problems in middle school, very often the solutions are irrational.

In which case it could say "no rational solutions found"

Yeah, I could also write a program that checks if all solutions are 0 and output the factorization, otherwise say "there are non-zero solutions". That's far from "a program that factors polynomials".

If you brag about how "you can design a computer program to factor any polynomial equation string input to it" in a class about quadratic equations and your code can't factor x^2 - 2, that's just not very impressive, regardless of your age.

Re: Teenager solves stubborn riddle about prime number look-alikes

#245

Post by khazhoux »

vcxy wrote: post #239
khazhoux wrote: post #192

Earlier quoted context omitted.

eh, I'll let my comment stand on its own ;-)

It definitely does stand on its own, haha. I appreciated it anyway

Thanks. Glad at least one person got it :-) I took a risk with the subtlety!

Re: Teenager solves stubborn riddle about prime number look-alikes

#246

Post by RC_ITR »

Huh1337 wrote: post #216
RC_ITR wrote: post #202

Earlier quoted context omitted.

Sure if you want the student to never be around same aged peers and struggle to develop a social life so they instead focus on their work, I agree.

The opposite causes the teacher as well as the peers to resent the more intelligent child, so which is better? I could read since I was 4. When others at school were reading one word per minute spelling letter by letter, I finished the whole article and then continued to another and another. Result? I got a teacher's note (a big deal where I live) almost every lesson, and bad grades. And the children hated me, probab…

I'm sure it was very hard for you to be a genius surrounded by dunces and I'm sorry those dunces didn't like you for no reason.

Re: Teenager solves stubborn riddle about prime number look-alikes

#247

Post by RC_ITR »

lmm wrote: post #211
RC_ITR wrote: post #202

Earlier quoted context omitted.

Sure if you want the student to never be around same aged peers and struggle to develop a social life so they instead focus on their work, I agree.

Students can tell who's smarter and who's not, and someone at the same level of learning will always be far more of a peer than someone who happens to be the same age. All the available evidence is that the best thing for children's social life is to let them interact with people at the same learning level rather than the same age. (To say nothing of the fact that segregating students by age is unnatural in the first…

You know what else is natural? Dying of polio

Re: Teenager solves stubborn riddle about prime number look-alikes

#248

Post by RC_ITR »

BeFlatXIII wrote: post #222
RC_ITR wrote: post #202

Earlier quoted context omitted.

Sure if you want the student to never be around same aged peers and struggle to develop a social life so they instead focus on their work, I agree.

Would they have success at developing a social life if they were surrounded by same-aged peers of average intellect? It'd be a crapshoot.

I mean sure, Hacker News is proof of that, but most hyper successful adults that were prodigies went to places like Exeter, Andover, Stuyvesant, Boston Latin, Bronx Science, etc. where they are around smart people their age.

Re: Teenager solves stubborn riddle about prime number look-alikes

#249

Post by RC_ITR »

Zababa wrote: post #229
RC_ITR wrote: post #202

Earlier quoted context omitted.

Sure if you want the student to never be around same aged peers and struggle to develop a social life so they instead focus on their work, I agree.

Being at the same ability level matters way more than being at the same age. Speaking from personal experience, the whole "let's try to pretend that this kid is normal and that with enough time he will fit in" has had terrible consequences on my mental health, and even on my social ability with the rare people that I feel comfortable with. I think that in many case, trying to pretend that people are the same when the…

You realize there are plenty of places like Exeter, Andover, Stuyvesant, Boston Latin, Bronx Science, etc. full of genius children, right? I agree those places are much better than a given average High School.

The problem is putting a child in an environment where they are surrounded by adults all the time. Like being 17 and having your 'peers' be 30 year old post-docs who are getting married and having children is a complete mind-fuck.

Re: Teenager solves stubborn riddle about prime number look-alikes

#250

Post by NoImmatureAdHom »

dekhn wrote: post #238
tylerhou wrote: post #183

Earlier quoted context omitted.

(Note: "inheritable" here is not exclusive to inherited genetics; it also refers to upbringing.)

Generally, heritability refers to genetics, not upbringing. Specifically: "amount of phenotypic (observable) variation in a population that is attributable to individual genetic differences" It wouldn't make much sense to report things that were related to upbringing together with genotype, as those are specifically the two things you want to decompose.

Yeah, dekhn you're correct. There are mechanisms of inheritance that aren't genetics (like heritable epigenetics, maternal effects, etc.), but when we're talking about "heritable" the vast majority is genes.
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