Ghideon

What is the mathematical expression* of this error? Given the mathematical expression for the error, provide an expression for the range. *) Not a numerical or visual example in a graph

Integer factorisation is defined within the integers (Z) and depends on integer divisibility. A relation that yields non-integers cannot represent or detect factors. Your formula (((pnp^2/ x ) + x^2) / pnp) yields non-integers (except for some trivial case). Hence your equation is algebraically invalid as a method for finding primes or factors.

Can answer the question I asked above? How? Please show mathematically step by step what you mean. Use the symbols and derive the result. (Do not use any numerical example) Note the bold part

From the paper you linked "the rise of AI systems that can convincingly imitate human conversation will likely cause many people to believe that the systems they interact with are conscious." That is one aspect of the illusion I pointed out above. The paper also does not mention "Vedanta" so I do not see the connection to your ideas

Then you understand how interaction with an LLM works: the model itself has no memory or state across calls? The illusion of dialogue comes from sending the full context with each request.

Is it a surprise that the LLM hallucinated and failed to follow the prompt? Also the prompt example I posted is intended as input to an LLM; not an LLM wrapped in some software where additional information is inserted (except for system prompt(s) )

Give me a definition of consciousness in a Turing machine and I'll create a test for it. When you discuss AI you do not talk about human intelligence so I guess "consciousness" to you means some kind of artificial variant, a simulation or a model implemented in software ad running on contemporary hardware. Note that there are several tests available for humans and definitions such as Glasgow Coma Scale. But that has of course nothing to do with Artificial Intelligence.

Here is a simple prompt I used, inspired by the auto-complete comment from @TheVat

Ok. But what is the point? Any LLM prompted to simulate consciousness will generate text consistent with the prompt but this is only probabilistic token prediction; not actual consciousness.

Yes I tested. The quotes are output from ChatGPT. DeepSeek-R1-Distill-Qwen-14B locally installed gives similar results with temperature 0.7.

Thats a good way to say it. Two examples to illustrate the autocomplete in this context @Prajna: Assume we ask an LLM to complete the sentence "As we all know it is proven beyond doubt that the most advanced LLMs today are conscious, as shown in" then the LLM could output the following incorrect output: Of course, in reality, this is not proven at all it’s just the model echoing the framing of the question. Second example; a work of fiction: Only difference is the context; the prompts before input asking the LLM to autocomplete.

What you describe is an interpretation of the model’s text that aligns with your view of consciousness, not evidence that the LLM itself has subjective awareness.

How? Please show mathematically step by step what you mean. Use the symbols and derive the result. (Do not use any numerical example)

I know of Euclid's method and its use in cryptography; I got curious since I don't see an obvious connection to trurl's approach ("multiplying by 5"). Can you elaborate on the relation to Euclid's method?

So you do not know? Not even a rough estimate? So you do not know? Not even a rough estimate? RSA-260?

In your example; how many numbers do you need to store?

Can you present an example, how is Euclid used in your method? How it is related to your " multiplying by 5"?

I'll try again, providing different answers since the questions are different There exists many algorithms to factor semi primes. I have to assume that "reliable" means "deterministic" in contrast to probabilistic. An example is trial division; for any given semi prime n=p*q (p and q primes) trial division will always find the factors. It is 100% reliable; there are to semi primes n where the algorithm produces incorrect factors*. GNFS is another algoritm.** A semi prime is the product of two primes. Finding semiprimes can be done by iterating through lists of prime numbers and multiplying them. That is again a different question. Trial division and GNFS have no upper bounds; any finite semiprime can be factored by the algorithms. It does not matter if the semiprime is large, the algorithms will eventually terminate and produce the correct factors. Then of course is the practical question; how you define "large", can large semipimes be factored given available resources (time and computing power). Factoring a semiprime that is the product of two large primes of similar sizes is inefficient and practically impossible if n is large enough. How this is related to your idea about multiplication and working with 5*n i have no clue. The cartoon still explains the situation. *) of course assuming algorithm execution is correct. **) General Number Field Sieve; the most efficient currently known algorithm for factoring

What do you mean by find semiprimes?

Your ideas about prime numbers may have some use in a work of fiction, poetry or similar. Or maybe in computer education; "find one major flaw in this attempt at an algorithm (correct answer: the unnecessary multiplication)"? In mathematics, where this is posted, I fail to find your ideas about primes useful. What if? As I said above: There are many reliable methods for factoring semiprimes.

Introduction to AI usage for legal professionals. Your example is interesting because it is easy to relate to and also opens for multiple lines of reasoning about generative AI. 1: We know an answer exists; the episode do exist and it has music. But it may or may not be included in the training data for the model. The music may be unreleased 2: There are many different ways to search for the answer, depending on what one knows about the episode, the music or other details that allows a model to infer an answer. Multimodality comes into play; does the model infer the answer from text only, or also audio and video? 3: If the model inference fails; what does it output? In the context of this thread (and in my presentation) is the response "intelligent" or at least useful? 4: Context; how does the level of detail provided to the model affect the answer. Note: In this specific case I did a quick test and it failed to find the music even with web search enabled. But I got a possibly useful explanation of why it failed* and a suggestion**. *) Short extract: custom/production-library needle-drop (or bespoke cue) cleared for the episode but not commercially released. *) contact the musical supervisors. (The AI got the names from the credits of the episode)

Not necessarily a bad analogy but logically it works only if you already know that the original number (let's call it n) is prime (and hence have no need for a test)? If n is semiprime the multiplication results in a larger composite making the test slower than running the (hypothetical) algorithm on n. Also note the state of the art algorithms for primality tests are extremely fast compared to composite (or semi prime) tests. (I resented comparisons in an earlier post) It would certainly be of interest in cryptography? Since for instance RSA build on the fact that testing for prime is easy compared to factoring.

May I ask what you used as input in your searches? (Curious; it may be an useful example in a work-related presentation)

The above makes sense. The rest does not. Take a look at the cartoon I posted.

Hello! Maybe, it depends on what you would like help with. The title "Black hole Paradox Solved!" sounds like a claim rather than a question?