Ghideon

This seems like homework so I'll give some hints. - Some values may be trivially incorrect, which ones can you eliminate? - Are you familiar with any equations that could be used? Acceleration is known to be constant and initial velocity is zero (car starts from rest)

At least this comment seem illustrate your belief How many numbers do you have to test? (answer: too many when the semi prime is of realistic length) How long does the test take? (answer: very long when the semi prime is of realistic length) Have you reduced the amount of numbers that needs to be tested. (answer: no) You just need to check my description of how 0.25 is a limit and how I am correct on this. And a quick look at the graph and/or a binary conversion of the smallest of the factors of RSA-100 supports my statement. Feel free to ask for clarifications. I don't understand your claims at all. Obviously the graph tells us that 0 < x < 1051 which is already trivial given that the semi prime is an RSA number. Your graph gives no new information and is therefore not useful. What you say is already trivially known without your graph. The central part of the problem is just swept away without any explanation: It is just that the numbers of factor are huge and no improvement is presented which means that RSA (and similar methods ) is unaffected.

Sorry, the description does not seem to match the link. I see you use RSA-100 but not what the other means. Sorry, I have no clue what this means. The opposite seems true; y=0 means x is not a possible prime factor. But it does not give any information about factors. Throwing a dice would be even quicker and give the same amount of information (zero). I still have no clue what you expect someone to see that has a connection to actually finding factors of a semi prime. But it supports my note above about the lover limit of 0.25 of large semi primes related to RSA. (We can see this since RSA-100 factors are known by adjusting the plotted x-values)

That seems to be equivalent of "I don't know". If no observation or calculation can distinguish between the two options then I think your idea is invalidated. Sorry I was unclear, I meant: please provide a detailed calculation, better than my example, of how fast neutron stars shrinks in comparison to earth in your idea. Additional question: Does this mean that you think the event horizon of a black hole shrinks?

EDIT: Language issue; I confused Milling with Drilling. My comments below may not apply at all! Intuitively* I would do the opposite; very slow motion to slice through rather than try to drill. Success might depend on how much work you plan to do; doing many and/or deep holes could be rather time consuming if going slow. If available a hollow drill** might work better. A pipe with sharpened edge might work if hollow drills are not available. I would try to avoid regular (spiral) drills in soft materials, it could get stuck, tearing the soft material rather than cutting. Fast rotation makes it tricky to stop fast enough, increasing the risk. Some other possible options depending on the situation: If the material is reasonably thin and holes are small I would try a Single-hole punch (for leather, cloth, or thin plastic). Thin material and larger holes: Hollow Punch If material is soft and does not take damage; compressing it and drilling or cutting through might work If precision is required it might be an option do do a silicon mold around pins instead of drilling holes *) Note I've never drilled though silicon but have some experience with having to improvise with tools or use them in unorthodox ways, hence I share an opinion even without having an experience from the exact situation. **)video showing how to sharpen a pipe, using it as a hollow drill to make a hole in rubber: https://www.youtube.com/watch?v=yQ-s0sBMHig

So which one of your options are correct and which one is incorrect? Ok. Please provide a calculation with better precision than my example.

Advise: Try to explain your stuff, it is your stuff that makes no sense. Anyone interested in this thread already knows* about RSA and encryption. (Bold by me) This is clearer than before but still a claim and not yet an explanation (or evidence or mathematical proof). And as far as I can tell (also see the mathematics I provided) you do the opposite; making harder or impossible. I must admit that I'm not interested enough to try to provide an explanation or attempt at a mathematical proof. Sorry, it does not make sense. *) Or will ask questions here or in separate threads or read elsewhere.

Is that of interest even if the mathematics shows that your idea is incorrect?

Thanks @MigL! I did not think of that, it seems to present us with a neat way to falsify the idea using a simple ballpark* calculation. Neutron stars average density is 1014 times the average earth density so neutron stars shrinks by 50% in about 1 hour by following the logics presented by OP. Even with an error margin of 10.000, all neutron stars would take about one year to reach 50% of it's original size. Since no neutron star out of the 3,200 known neutron stars in the Milky Way and the Magellanic Clouds** have displayed anything like this behaviour the idea presented by OP is incorrect. Case closed. *) The vague descriptions from OP prevents any detailed or exact calculations. **) https://en.wikipedia.org/wiki/Neutron_star

You said: Please present a consistent explanation. Seems like we now have "can depend", "can't depend", "does depend" and "not sure"

Sorry, the provided explanation is not better. This is one of the contradictions in your descriptions: If it is a one-way function then you are guaranteed to fail to find the factors of a given large integer as used in RSA. You seem to use an approach that require that it is not a one-way function. *) One-way function - Wikipedia

No, 0.25 is the lover limit because of assumptions regarding primes used in RSA. Everything is in the mathematics above* where I compared your expression to typical numbers used in RSA. Feel free to ask for clarifications or for more details if needed. (I have no clue what you try to solve or do with your musings on prime numbers, your explanations does not make sense. I adress the posted claims regarding RSA.) *) https://www.scienceforums.net/topic/124453-simple-yet-interesting/?do=findComment&comment=1218729

Objects shrink at different rates according to you. Ok, but you said shrinking is greater where gravity cancels, between bodies. No such observer can exist; where gravity cancels the shrinkage is great: Explanations are so far inconsistent to such a degree that it is hard to take the ideas seriously*. Is this idea some kind of joke? *) By "seriously" I do not mean credible in comparison to established models, just serious enough to be worthy of a scientific discussion with the intention to learn something.

The above statement contradicts your earlier response: (When asked about if Jupiter should shrink faster than mercury due to the different strength of gravity.) Note that "distance" and "radius" does not make any sense; you claim everything is shrinking so you need to account for passing of time, relativity and effects of shrinking, both the observer and the observer objects? Also note that you need to take into account that the constants, as a consequence of your explanations, are not universal constants so G does not apply. But it's not that important, it can wait until we have some evidence supporting your claims. Or at least have some explanation that is consistent enough to be verified against observations?

Bold and so far unsupported. This is confusing ,what is less than zero? The expressions you posted returns positive numbers*. I'm still referring to your expression [math]\frac{ x^{4} }{ pnp^{2}+x }(pnp=x*y, x<y) [/math] How? RSA is about the product of 2 large primes as far as I know. Compared to what method? Again you post an image so it can't be quoted. It's confusing; I don't see any negative numbers in the picture, and I do not see x in any expression and there are some errors in the statements. Would you mind commenting on the fact that 0.25 is the lower limit of your expression [math]\frac{ x^{4} }{ pnp^{2}+x }(pnp=x*y, x<y) [/math]? Clarification & details: Prime numbers x and y, realistically used in encryption, would be large and of similar size for instance n bits (typically n>512). The smallest such number x would be the smallest prime larger than 10...02 and the largest number y would be the largest prime less than 11...12. So the two primes can differ by most 2n-1. Minimum difference y-x is 2 if x,y are prime twins. This results in the your expression having limits: [math] 0.25 < \frac{ x^{4} }{ pnp^{2}+x } < 1[/math] where [math] (pnp=x*y, x<y, x>0, y>0)[/math] , x and y are primes and requiring same number of bits for binary representation. This provides the mathematics needed to show that your approach, as far as it is possible to understand it, is incorrect. As long as you guess numbers that results in your expression being close to zero (<0.25) we are guaranteed that you are guesses are wrong in RSA. *) The mainstream definition is that prime numbers are positive so x>1 and y>1

Sorry @joao c h barcellos, the explanations does not make any sense. You seem to be mixing "shrinking" and relativistic length contraction? You also seem to mix "absolute" and "relative". Note that the force of gravity falls of with r2, the gravity differs quite a lot depending on location. For instance the gravity is much stronger at the surface on earth than on the surface of an astroid. The gravity from the rest of the galaxy is negligible in comparison to the gravity on the surface of celestial bodies. Hence, according to your logic, properties of old material on the surface of celestial bodies of various size should differ greatly. Ok, then it is many order of magnitudes less in interstellar space? And the sun, according to its higher gravity, shrinks much faster that earth? Easy check:tThere should be obvious density deviations in meteorites?

Yes, I know. That's why it is in my calculation above. That does not make sense. Can you express it mathematically? I've already provided you with a general calculation, see the lover (0.25) and upper limits (1)). You can get the expression arbitrarily close to zero by using any sufficiently large numbers where x<<y. That means that the closer you get to zero in your expressions the more wrong you are if finding RSA related primes is you goal. That insight should be trivial if you are familiar with RSA?

I still do not see any practical or useful connection to RSA. Assuming realistic RSA keys* and your definition** [math](pnp=x*y, x<y)[/math] then [math]0.25 < \frac{ x^{4} }{ pnp^{2}+x } < 1[/math]. That gives no new information about the prime factors x and y, in RSA only x*y is known. *) Using two large prime numbers of similar length. **) It's hard to understand the picture, some guesswork required.

Clarification/Correction: should be "younger", not "your" (too late to edit post)

Thanks, but it does not my question. What physical process happens when gravity shrinks particles? Ok. Earth (and other celestial bodies) is full of old particles that have spent long time in different gravitation so you comment implies that now there is a mix of particles with various size? Protons for instance should, as a result of your explanation, vary in size depending on their history of exposure to gravity. To the best of my knowledge no such differences are observed. Why? Accelerated particles does not shrink*. Ok. But: There should be great differences since gravity differs within the galaxy and in the solar system? For instance Jupiter should shrink faster than mercury or astroids do, over billions of year, due to the different strength of gravity. Note that rocks on the moon have been in lower gravity for long time vs old rock on earth. Why do samples of moon rock not deviate physically? Then old stars should emit light in shorter wavelength than your ones. And stars evolving in weaker gravitational fields should have different spectrum than ones evolving in stronger gravitational fields. It should be easy to see when observing a massive vs. a less massive galaxy; the star light should differ? Are there any supporting observations? *) Note: Length contraction (and time dilation) in special relativity is not particles shrinking

How does this happen according to your ideas? What physical process takes place, allowing this to happen? What happens on atomic and subatomic scales? What happens to (small) objects in free fall vs objects on the surface of a planet such as the earth? Do composition of meteorites or moon rocks support your ideas? I'm thinking over a time of billions of years; how has the size of planets, the sun, small space debris and the orbits been affected?

@joao c h barcellos were your answers mixed with my questions? please don't quote me with things I did not say.

Some quick questions to start a discussion. Per your ideas: What happens to mass and density as a result of local space shrinking? How has this shrinking affected the solar system and planetary orbits? What happens in strong vs weak gravitation? Does observations and comparison of sizes of relatively nearby vs distant galaxies support your idea?

Extract from your picture: It says x is semiprime.

Triggers my curiosity. Reading first line, "where pnp..." it is a contradiction. (Note: can't quote a picture) Ok, nothing new since early 2021: