Yeah I was gonna say the same thing. So in a base-6 counting system primes must be very intuitive to spot. Although also expanding it out to base-12 shows the primes always fall into 4 specific rows.

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madcaptenor 3 days ago | parent [-]

It's similar to how in base 10 all primes must have last digit 1, 3, 7, or 9. But it woks slightly better in base 6 because fewer numbers are candidates (2/6 ~ 33% instead of 4/10 = 40%)

	▲	AnotherGoodName 3 days ago \| parent [-]
		Yep and you can also just keep going with this to get to the Prime Number Theorem. If you just consider odd numbers you know that at best only half of numbers can be prime. We've ruled out 1/2 of numbers. If you then multiply 2 x 3 to get 6 you can state all prime numbers above 6 are of the form 6n + [1 or 5], everything else is a multiple of 2 or 3. We've now ruled out 1/3 more numbers in that remaining half we already ruled out above. Leaving 1/2 x 2/3 = 1/3 numbers possibly being prime (you could write this in a non-simplified form as 2/6 to match the count above). If you then multiply 2 x 3 x 5 to get 30 you can state that all numbers above 30 are of the form 30n + [1,7,11,13,17,19,23,29]. The rest are multiples of 2,3 or 5. You've now ruled out another 1/5 of numbers from that remaining 1/3 above. Leaving 1/3 x 4/5 = 4/15 numbers possibly being prime (or 8/30 if you don't simplify the fraction to more clearly match what we counted above). If you continue this you have a series that's multiplicative_sum( 1 - 1/p) of all primes so far. This function is called Euler's product formula and is the inverse of the famous Riemann Zeta Function (1/ζ(s)). This series converges to the Prime counting function https://en.wikipedia.org/wiki/Prime_number_theorem#Non-vanis... which you can intuitively understand from what i've written above. Fwiw these patterns in prime numbers, or more specifically the gaps where numbers can't possibly be prime, are extremely well understood. They were first documented by Erasthosenes in BC times who used the above to quickly find new large prime numbers. While it's fun to look at patterns in primes and any enthusiasm should be encouraged i will take a moment to point out that mathematicians occasionally deal with lay people who think they've stumbled on some revelatory new thing by observing these well known patterns in primes. There's a myth that 'there's no patterns in primes'. But... that isn't true at all. We know there's patterns. It's the basis for prime number theory. It's been known for a few thousand years now.