Ciro Santilli @cirosantilli 37

Ciro Santilli 37 Updated 2025-07-16

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Type of microscopy by

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Inflection by

Ciro Santilli 37 Updated 2025-07-16

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Perfect information by

Ciro Santilli 37 Updated 2025-07-16

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Admissible prime k-tuple by

Ciro Santilli 37 Updated 2025-07-16

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Twin prime by

Ciro Santilli 37 Updated 2025-07-16

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prime-number-theorem by

Ciro Santilli 37 Updated 2025-07-16

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Consider this is a study in failed computational number theory.

The

n / l n (n)

approximation converges really slowly, and we can't easy go far enough to see that the ration converges to 1 with only awk and primes:

sudo apt intsall bsdgames
cd prime-number-theorem
./main.py 100000000

Runs in 30 minutes tested on Ubuntu 22.10 and P51, producing:

Figure 1.
Linear $π (n)$ vs $n / l n (n)$ approximation plot
. $f (n) = n$ and $f (n) = l o g (n)$ are added to give a better sense of scale. $l o g (n)$ is too close to 0 and not visible, and the approximation almost overlaps entirely with $p i$ .

Figure 2.
$π (n) - n / l n (n)$
. It is clear that the difference diverges, albeit very slowly.

Figure 3.
$π (n) / (n / l n (n))$
. We just don't have enough points to clearly see that it is converging to 1.0, the convergence truly is very slow. The logarithm integral approximation is much much better, but we can't calculate it in awk, sadface.

But looking at: en.wikipedia.org/wiki/File:Prime_number_theorem_ratio_convergence.svg we see that it takes way longer to get closer to 1, even at

1 0^{24}

it is still not super close. Inspecting the code there we see:

(* Supplement with larger known PrimePi values that are too large for \
Mathematica to compute *)
LargePiPrime = {{10^13, 346065536839}, {10^14, 3204941750802}, {10^15,
     29844570422669}, {10^16, 279238341033925}, {10^17,
    2623557157654233}, {10^18, 24739954287740860}, {10^19,
    234057667276344607}, {10^20, 2220819602560918840}, {10^21,
    21127269486018731928}, {10^22, 201467286689315906290}, {10^23,
    1925320391606803968923}, {10^24, 18435599767349200867866}};

so OK, it is not something doable on a personal computer just like that.

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There are infinitely many Pythagorean triples by

Ciro Santilli 37 Updated 2025-07-16

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Direct consequence of Euclid's formula.

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Classification of Pythagorean triples by

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en.wikipedia.org/wiki/Pythagorean_triple#Generating_a_triple

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Fermat's last theorem by

Ciro Santilli 37 Updated 2025-07-16

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A generalization of the Pythagorean triple infinity question.

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TeachMeAsap.com by

Ciro Santilli 37 Updated 2025-07-16

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They sent one of the rare spams Ciro actually was interested in!!! Likely going down lists of top Stack Overflow users.

They have some kind of cryptocurrency, TCHME token, as a reward. Ciro wonders if the value of TCHME will ever be high enough to serve as a valid incentive.

Also, what is the total TCHME supply? Can the website devs issue as much as they want? They do giveaways e.g. as shown at: twitter.com/TeachMeAsap/status/1621353671840899072

And a centralized system with a certralized marketplace would work just as well for the initial phases. But fair play, the idea is interesting.

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Parody religion by

Ciro Santilli 37 Updated 2025-07-16

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Robot simulator by

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Rock musician by

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List of static site generators by