``` 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?