this is about a prime number generator can actually be done by just using TTL logic .. :D

and ..

it's about, GENERATE ANY of them
( not just fermat or alike and specially not, using any sieve technique )
it will fire them out one by one .. just like generator actually means ..

the only exception is
not to be able to jump to a specific N occurrence of a prime
because a bit more complicated while still feasible in theory ..

To get you in a correct perspective and avoid you to fall,
for the wrong assumption (as usual),
which will make you believe I'm just a lunatic which don't know what is talking about ..
let me point out something about me ..

1. the very first computer I did ever use ( much too expensive to own )
   was not even using a CPU, instead it have had 2 TTL boards ( PUCE1 and PUCE2 ) https://en.wikipedia.org/wiki/Olivetti_P6060

2. in 1991 when most CPU where still in 8/16 bit era, and parallel multiplier was still only present in specialized chips ( math coprocessors) I did design a very revolutionary new CPU .. (Inspired by a CPU created few years early,
   (ARM, the CPU that most likely (99.9999%) is in your mobile device right now))
   I did never publish my work on this, cause was much too early and then,
   the industry much too corrupt later on ..
   let aside you still mostly stick to 32 bit operations ..
   my design would only get effectively relevant starting from 32 bits ..
   and they were still counting each single transistor on the chip ..
   while today the transistors count goes in the order od BILIONS per chip

3. despite the so high number of transitor fits in a CPU today
   they are mostly useless in term of actual computational power
   your CPU still does most of it's main job by 'software' and with a very low level of parallelism
   except very specific cases , while most of the huge ammount of transistors in your CPU are dedicated to
   avoid bottle neck with peripherials (RAM , HDD , software loops etc .. ) (aside to heat up ,your room :D )
   it seems unbelieveable, but,
   30 years later CPU are millions of times more powerful in theory
   while they actually still stick to same procedural way to work ..
   and you got to wait for them just like 30 years ago .. **LOL

the most hilarious of all this
is that in fact prime numbers DON'T really exist .. period.

how is that possible ? well .. short answer,
Math PPL don't really understand Math .. ( or better said , they don't understand what they actually do when use Math (which is just a tool))

they get into a cult very soon, thinking Math can answer everithing by solving equations LOL fact is .. prime number exist just because the rule they made for them to show up .. (yep!)
that is, the entire cahotic progression which leads to so called prime numbers get to be special
is intrinsic in the "only divided by themself and 1"
( which BTW should be considered instead the very one prime numbers given that either 1 and itself is the same
however this would lead to no prime numbers at all which break their FAITH in Math GOD .. )

One is de facto generator of any other prime number .. ((YEP just as simple as that!!))

the progression then is just keept alive by 1, while others numbers
just contribute in cancelling out some of them periodically ..
2 will cancel out any even number making any odd number being potentially prime
which in fact is true till 9 when this one got cancelled out by 3
as it is 15 , 21 ,27.. etc .. ( notice 9 = 33=3^2 , 15=35 , 21 37 , 27=39=3^3 )
which in turn means primes up to 30 are ruled just by 2,3 ( being 1 the generator )..
only exception is 25 which is again 5^2 ..

there's NOT anything really special about prime number except they are unpredictable by
some stupid math function f(x) .. just like any other cahotic progression, can't be reduced to a linear imaginary Math relation .. this doesn't make them unpredictable .. just a bit more complex than what Math PPL ASSUME the world is ..

they just follow a precise chaotic progression ..
can be predicted and splitted into repetitive patterns just like any other chaotic/fractal ..
however if you BELIEVE numbers come out of nowhere and have no relation between them
you are left to some stupid sieve / factorization to find them as they where put there by GOD himself LOL

BTW ,
I always knew this since child , that's why I DID NEVER use factorization,
cause was clear since then, it was just a sort of CULT ..
you don't really need primes to solve any actual Math problem .. unless you adore them as a GOD sign LOL