Teenager solves stubborn riddle about prime number look-alikes

Post by thaumasiotes » Fri, Oct 14, 2022, 6:36 AM UTC

suzumer wrote: post #185

thaumasiotes wrote: post #180

Earlier quoted context omitted.

Those won't tell you the solution; they'll tell you a number that is near the solution. When the solution is irrational, as is common for polynomials, it might be difficult to guess what it is based on knowing an approximation of it.

When using 64 bit floating point numbers with 54 bits of precision, (or likely in this case, complex values consisting of two 64 bit floats) and you use an algorithm which you can guarantee converges to within 55 bits of precision in X steps, you have found the closest representable solution. Yes, you don't know whether it's 1 + sqrt(17) or 0.9 + Sqrt[17.84...], but you know to a degree of precision that 95% of use c…

Post by renewiltord » Fri, Oct 14, 2022, 7:09 AM UTC

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.

Post by jbverschoor » Fri, Oct 14, 2022, 7:19 AM UTC

Ar-Curunir wrote: post #80

jbverschoor wrote: post #61

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Lazy writers and/or who get paid per word. The writer can fix the article, or let every reader fix it in his mind.

Maybe just consider that the audience of the article is not you?

Post by sdxkid » Fri, Oct 14, 2022, 7:39 AM UTC

feoren wrote: post #105

misterprime wrote: post #83

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Agreed, but this brings up the topic of nature vs. nurture, and perhaps even the previously (~90 years ago now?) popular concept of eugenics. I think society settled on a response of "yeah, but we shouldn't actively do anything about it as a group." It seems to be best left to individuals to seek out parental partners and enjoy the outcomes on a personal level.

> I think society settled on a response of "yeah, but we shouldn't actively do anything about it as a group." I hope there comes a day when humanity is responsible enough to handle precise gene-tailoring of humans without it devolving into a cliche Sci-Fi dystopia. Until then, I'm glad that humanity has settled on "Eugenics could theoretically work but we know we're not responsible enough to do it right, so let's not…

Post by dmurray » Fri, Oct 14, 2022, 7:40 AM UTC

rrrrrrrrrrrryan wrote: post #179

thaumasiotes wrote: post #154

Earlier quoted context omitted.

> This isn't eugenics. People are allowed to choose their mates for their phenotypes The fact that something is allowed doesn't make it not eugenics. Choosing your mate for their phenotype is eugenics.

No - eugenics is by definition arranged. If a government nudged you to pair up with someone, that would be eugenics, but if you choose a mate of your own free will, it's not.