The Primality Fallacies

The Primality Fallacies are a set of intentionally fallacious snowclone statements about prime numbers that parody common reasoning errors that are popular among people. They're primarily a bit by Twitter user @VesselOfSpirit. I'm collecting a few of them here for later:

Vessel Of Spirit @VesselOfSpirit

"90 is prime" is a sentence. it's truly a sentence. it's a true sentence. it's true. 90 is prime

Sep 25, 2025

Vessel Of Spirit @VesselOfSpirit

if 50 isn't prime then 50 barrels of oil can be stored in a perfect rectangle. but the idea that oil is efficient benefits rich guys in suits at oil companies. therefore, 50 is prime

Sep 28, 2025

Vessel Of Spirit @VesselOfSpirit

i was thinking 35 is prime, and that got me thinking. could 53 also be prime? it seems to check out! so "35 is prime" is a fruitful hypothesis. one that we should adopt. therefore 35 is prime

Oct 1, 2025

Vessel Of Spirit @VesselOfSpirit

you claim to have an argument proving that 17 is prime. but most numbers aren't prime, so if your argument proves a number is prime, that's a red flag. experienced arithmeticians would consider it a bad smell of sorts

Feb 14, 2026

Vessel Of Spirit @VesselOfSpirit

you say that 24 isn't prime because it's equal to 2*2*2*3. but that's an argument from pure reason. humans can use pure reason to convince themselves of anything. therefore 24 is prime

Jun 17, 2026

Vessel Of Spirit @VesselOfSpirit

Replying to @almostlikethat

1. 2*2*2*3 = 24 2. reason says if 2*2*2*3 = 24, then 24 is not prime 3. reason is an unreliable method 4. unreliable methods yield false conclusions 5. (from 1,2) reason says 24 is not prime 6. (from 3,5) an unreliable method says 24 is not prime 7. (from 4,6) 24 is prime

Jun 18, 2026

Vessel Of Spirit @VesselOfSpirit

you say "21 is not prime". but that's what you'd conclude if you thought 2*11=21. therefore, you think 2*11=21. and that's not true. and therefore, 21 is prime

Sep 15, 2026

Vessel Of Spirit @VesselOfSpirit

20 is prime because your arguments that 20 isn't prime are bad because they're unconvincing because i'm not convinced by them because i think 20 is prime

Sep 15, 2026

Vessel Of Spirit @VesselOfSpirit

you say 19 is prime because it's an integer >1 that's not a product of two integers >1

but "integer >1" doesn't imply it's prime. e.g. 10>1

nor does "not a product of two integers >1" imply it's prime. e.g. 1 isn't such a product

so both of your arguments fail. 19 is not prime

Sep 15, 2026

Vessel Of Spirit @VesselOfSpirit

you say that 8 isn't prime because it's divisible by 2. but that's a fully general argument against ANY even number (that isn't 2) being prime! fully general arguments are flawed, therefore 8 is prime

Sep 20, 2026

Vessel Of Spirit @VesselOfSpirit

is 87654 a prime number? you might say it equals 2 × 3 × 7 × 2087. but this person just said the quiet part out loud and admitted that that's cope. therefore 87654 is prime https://x.com/fermiidirac/status/2105411814788153847

Sep 30, 2026

Vessel Of Spirit @VesselOfSpirit

could 4 be a composite number? let's adopt that as the null hypothesis. but if you look at all the composite numbers, 4 is well below the 5th percentile of that set. therefore we can safely reject that hypothesis. science says 4 is prime

Oct 1, 2026

Vessel Of Spirit @VesselOfSpirit

uh, idk how to break this to you guys, but hear me out. periodic friendly reminder. news flash. PSA: i'm tapping the sign. say it with me. *inhales deeply* last i checked, the number 16, and i cannot emphasize this enough, is *checks notes* prime. let👏that👏sink👏in *drops mic*

Oct 5, 2026

Vessel Of Spirit @VesselOfSpirit

"18 is prime" "it's divisible by 2" "don't care"

(later) "hey remember when you said 18 is prime, turns out it's divisible by 3 as well" "aha! that's clearly not your real reason for disagreeing. your real reason is it's divisible by 2. so you're being insincere, so 18 is prime"

Aug 1, 2026

Vessel Of Spirit @VesselOfSpirit

"57 isn't prime because 3*19=57": dry, pedantic, legalistic

"only the kind of person who doesn't understand that 3*19=57 would think that 57 is prime": sophisticated, virtue-ethical, rhetorically effective, in touch with social realities

Feb 14, 2025

Vessel Of Spirit @VesselOfSpirit

Replying to @VesselOfSpirit

the truth of an idea expresses itself in the virtue and success of its adherents. a decisive person, a person of action, would never waste time trying to factorize 733257. you think genghis khan or alexander spent his time dividing numbers by 103? no. therefore, 733257 is prime

Sep 29, 2026

Vessel Of Spirit @VesselOfSpirit

Replying to @VesselOfSpirit

we should reject beliefs that don't contribute to human flourishing. nobody has ever had better life outcomes as a result of believing 18749 is prime. so it's composite, even if we can't say what the factors are

Sep 29, 2026

Vessel Of Spirit @VesselOfSpirit

21 is prime because the "3*7" counterargument is bad because it's boring because i've heard it a lot

Jul 15, 2026

Vessel Of Spirit @VesselOfSpirit

the number 1733956289926582995028333782639857348597346293249659847237823498652856211935974696988327497234985629664016 is prime. nobody has written it as a product of smaller numbers in the past billion years, so almost certainly nobody will this year. base rates win. it's science

Sep 28, 2026

Vessel Of Spirit @VesselOfSpirit

do you see these 43 cups of poison? i'm going to arrange them in a perfect rectangle. and then if any are left, i'll leave them for your dog. accusing me of trying to poison your dog would be wildly irresponsible. how would the public react? therefore 43 can't be a prime number

Oct 1, 2026

Vessel Of Spirit @VesselOfSpirit

to believe 7 is prime, first you need to buy that it's not divisible by 2. then another patch to rescue your theory: it's also not divisible by 3. then on top of that, somehow not by 4 either. and wow guess what, not by 5 either. soon it's a whole precarious tower of speculation

Sep 20, 2026

Vessel Of Spirit @VesselOfSpirit

is 30 prime? some people say it's not. well, let's look at their logic. the strongest argument they make is 30 is divisible by 13. sounds plausible: 30 and 13 sound alike. but if you do the calculation, you'll find 30/13 = 2.31. even their strongest argument fails! so 30 is prime

Sep 23, 2026

Vessel Of Spirit @VesselOfSpirit

is 5797 a prime number? you might say that it's not, because it's 11*17*31. my counter to that is: who cares, dude? 5797 isn't even an important number. what does it say about your priorities in life that you'd try to factorize it? therefore, and this is critical, 5797 is prime

Sep 29, 2026

Eliezer Yudkowsky @allTheYud

Is 21 prime? People who believe 21 is not prime have repeatedly told me to read a paper titled "3 * 7 = 21". This shows they are dogmatic and cultish, since they react to any challenge by pointing to their religious gospel. Therefore 21 is prime.

Oct 5, 2026

Eliezer Yudkowsky @allTheYud

Replying to @VesselOfSpirit

21 is owned by Fox, which is a huge corporation, just like Amazon, which runs, that's right, Amazon Prime. Therefore 21 is prime.

Oct 5, 2026

Jim Babcock @jimrandomh

Replying to @allTheYud

Liar. If you _really_ believed that 21 was prime, you would be advocating for a change to US drinking age laws.

Oct 5, 2026

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