``` Providing the full Brainfuck code to dynamically calculate and factorize 1000! is unfortunately not feasible, and here is why: * The Scale: 1000! (1000 factorial) is a number with 2,568 digits. Standard Brainfuck operates on 8-bit memory cells (values 0-255). To handle a number this large, one would first have to write an entire "arbitrary-precision" math library (BigInt) from scratch within Brainfuck. * The Algorithm: You cannot simply compute 1000! and then factor it. You must use Legendre's Formula to determine the exponent of every prime p \le 1000. * Formula: E_p(n!) = \sum_{k=1}^{\infty} \lfloor \frac{n}{p^k} \rfloor * Example for p=2: 500 + 250 + 125 + 62 + 31 + 15 + 7 + 3 + 1 = 994. * The first term of the answer is 2^{994}. The Solution (Python) Since Brainfuck is ill-suited for this, here is a Python script that uses Legendre's Formula to instantly calculate and print the factorization of 1000!. def legendre_factorial_exponent(n, p): exponent = 0 while n > 0: n //= p exponent += n return exponent

def sieve_primes(n): primes = [] is_prime = [True] * (n + 1) for p in range(2, n + 1): if is_prime[p]: primes.append(p) for i in range(p * p, n + 1, p): is_prime[i] = False return primes

def factorize_factorial(n): primes = sieve_primes(n) result = [] for p in primes: exponent = legendre_factorial_exponent(n, p) result.append(f"{p}^{exponent}") return " * ".join(result)

print(factorize_factorial(1000))

The Brainfuck Code (for 1000 not !) If you simply meant the number 1000 (without the factorial), or you just want to see what Brainfuck looks like, here is a program that outputs 1000: +++++ +++++ [ > +++++ +++++ < - ] > -- . (Print 100 'd') < +++++ +++++ [ > +++++ +++++ < - ] > + . (Print 101 'e') (This is just "d" and "e" for demo; printing "1000" requires ASCII conversion)

Correct code to print "1000": ++++++++++[>+++++>+++++>+++++>+++++<<<<-]>-.>-.>-.>-.

Explanation: * Sets cell #0 to 10. * Loops 10 times, adding 5 to cells #1, #2, #3, #4 (making them all 50). * Subtracts 1 from cell #1 (ASCII 49 = '1'). * Subtracts 2 from cells #2, #3, #4 (ASCII 48 = '0'). * Prints them. Would you like me to explain how Legendre's Formula works in more detail? ```

That's not true. From the little time I've spent trying to read and write some simple programs in BF, I recall good examples being pretty legible.

In fact, because the language only relies on those few characters, anything else you type becomes a comment. Linebreaks, whitespace, alphanumeric characters and so on, they just get ignored by the interpreter.

Have a look at this, as an example: https://brainfuck.org/chessboard.b

"Fast" models are mostly useless in my experience.

I asked "Gemini 3 Pro" and it refused to give me the source code with the rationale that it would be too long and complex due to the 256 value limit of BF cells. However it made me a python script that it said would generate me the full brainf*ck program to print the factors.

TL;DR; Don't do it, use another language to generate the factors, then print them with BF.

Absolutely not. Id bet a lot of money this could be solved with a decent amount of RL compute. None of the stated problems are actually issues with LLMs after on policy training is performed.

We use naturally evolved human languages for most of the training, and programming follows that logic to some degree, but what if the LLMs were working in a highly complex information dense company like Ithkuil? If it stumbles on BF, what happens with the other extreme?

Or was this result really about the sparse training data?

-> runs it in Gemini fast instead of thinking

....

Gemini Pro neither as is nor in Deep Research mode even got the number of pieces or relevant squares right. I didn't expect it to actually solve it. But I would have expected it to get the basics right and maybe hint that this is too difficult.

Instead in Pro Simple it just gave a wrong solution and Deep Research wrote a whole lecture about it starting with "The Geometric and Cognitive Dynamics of Polyomino Systems: An Exhaustive Analysis of Ubongo Puzzle 151" ... that's just bullshit bingo. My prompt was a photo of the puzzle and "solve ubongo puzzle 151"; in my opinion you can't even argue that this lecture was to be expected given my very clear and simple task description.

My mental model for language models is: overconfident, eloquent assistant who talks a lot of bullshit but has some interesting ideas every now and then. For simple tasks it simply a summary of what I could google myself but asking an LLM saves some time. In that sense it's like Google 2.0 (or 3.0 if you will)

Whereby I don’t know if it was a real infinite loop because I cancelled the session after 10 minutes seeing always the same "thoughts" looping