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My apologies, I chose 25 and 7 at random just to demonstrate the first part of the method. In the case of "f(25, 7) = 3", I'm not proving any number to be prime, I am nearly stating the result of the method previously described. In order to test for primality, comparisons must be made. If f(x, k) > f(y, k) where k is the first 100 or so primes (though any numbers can b used as k, there is a noticeable increase in accuracy when using primes over composite numbers) then x is more likely to be prime than y is. To answer your question about false positives, I wrote a method which computes the average result of f(x, [first 100 primes]) for every number from 1 to 1,000,000. Then if the result for any individual number is greater than or equal to 1.09 (1.09 is just the constant which seemed to work best, it could just as well be any number) * the average, it is considered to most likely be prime. This is because a number x who has a higher than average f(x, y) is more likely to be prime then a number with a smaller f(x, y). The results yielded 2745 possible primes, of which 361 were correct. This isn't truly the best way to use this method however, its really meant for taking a large list of large numbers and telling you which ones to test first for primality. Hopefully this clears it up, if not, I can write out some pseudo code so you can get a better feel for the algorithm.

I thought of a probabilistic primality test a while back and have looked online trying to find if this method has been used or described anywhere before, but so far haven't seen it anywhere. The basic idea is as follows: Define f(x, y) as the number of times “temp = y”, “y = x modulo y” and “x = temp” can be preformed before y is equal to 1 For example, f(25, 7) = 3 because 25 modulo 7 = 4 step 1 7 modulo 4 = 3 step 2 4 modulo 3 = 1 step 3 In general, using prime numbers as either x or y will result in a higher answer when compared to non prime numbers. This method isn’t exact by any means, and can only tell you which numbers are more likely to be prime, not which numbers are certainly prime. This method can be very useful in running through a very large list of potential primes and ranking them in terms of which ones deserve to be checked first for primality. It should also be noted that any two numbers of a close ratio to phi (1.618…) will also result in a larger than average result, for example 10 and 16, 100 and 162. In order to determine if a number k is more likely to be prime then another number t, compute the sum of f(k, x) where x is 2…n, where n is any number, the higher the number the more time the process will take but the more accurate the method will be, generally using anything around 1000 will yield decent results. If f(k, x) > f(t, x) for x in 2…1000, k is more likely to be prime than t. So my question is how useful could this method be? What is the efficiency of this algorithm? Is it O(1) because the largest order operation preformed is modulos? Has this been used before at all?

Great question. Something to consider is how one would simulate the entire universe, using what I'm assuming amounts to less then all the energy in the universe. You must use less then the total energy, because you and any other people relying on this machine would surely be made of energy. Thus the following question arrises: can X particles predict X + Y other particles (where Y is any integer above 0)? If not, the machine is impossible. However a close approximation may be made which could drastically cut down on the required energy to make such a machine.

Even if we assume for a moment that it is possible to have something that has no energy of any kind, how would you reach this state? Energy flows from high to low so reaching absolute zero would (please correct me if I'm wrong here) require something below absolute zero, or in other words, something that has a negative amount of energy. You can't get negative energy so this means that reaching that 0 energy level is not possible. Good question. I hope that this helps you and your friend.

Assuming that time is an absolute, fixed dimension, that doesn't mean we have to move through it at the same speed. The faster that we move through space the slower we move in time in relation to how fast we were previously moving through time. How would this idea of time being a fixed dimension account for photons, which theoretically experiance all moments of their existences instantaneously? In this idea of time having frames, photons would experiance seeing every single frame at once. Also humans don't need to have a time frame to experiance time. Human brains can only process information at a fixed rate, which is much slower then the speed of light and certainly not instantaneous. All objects exist in every time frame, just in different forms. The human brain is no exception to this. This means that the human brain experiences time just as the rate at which information is processed and time is flowing due to speed. To date, no way has need discovered to directly move from one point in time to another. This means that even if someone were to dramatically dialate their time frame it would still exist in the moment that the casual observer barley moving would still be able to see their faster moving friend. This, in my opinion, disproves your initial hypothesis, however I could have been wrong here so correct me if I was incorrect about anything.

At the risk of straying too far into philosophy, what do you define as real? I suppose that it could be argued that nothing is "real". Also, the job of scientists is not to find one "truth" and stick with it, but to try their hardest to disprove every theory possible in order to get rid of all incorrect theories. As strange said, I don't understand what unresolved issues you are referring to, please clerify that. I hope that this post helped, if something didn't make sence let me know so I can correct it. Excellent topic by the way.

I am confused about how some creatures can be clear, or at least mostly clear. One example is the clear squid (more commonly called the glass squid). How can their organs be clear, their stomachs must produce acid which I assume has some coloring. Surely their blood must not be clear, or is it? And most puzzling to me, how can they produce black inc when they appear clear? I thought that maybe they combined two clear chemicals to produce one black chemical but I wasn't quite sure. Perhapse this just stems from my misunderstanding of how squid work. Thank you in advance for all replies and your assistance to help me further understand this topic.

Well that depends on your definition I guess. If you mean reversing gravity, then your right, gravity is just (as we currently understand it) attractive. There are other means to defy gravity though, but when I jump I don't confused it anti gravity. Counteracting gravity, setting up a system where the effects of gravity are counteracted compleatly by some other force, could be called anti gravity.

Unless I'm mistaken compression waves among atoms are just the atoms getting very close, but not touching. So if the electrons in the atoms are repealing eachother, then by the time you compress something to the point of plasma, where unless I'm mistaken all the electrons are on the outside of the plasma body, then how could compression waves travel? Would the neucleus of each atom repel away from eachother? If this isn't how compression waves travel (with electrons repealing eachother and thus their atoms apart from eachother in a wave) then please correct me.

I'll try to further help out our idea of an atom. The electrons, as all particles, can be waves. As particles however they are almost entirely perfectly spherical. The electrons are quite far from the nucleus compared to their size...most of the time. Due to the uncertainty of where the electrons are, they generally stay near their orbitals, but sometimes are actually inside the nucleus (I might be wrong here but this isn't this called quantum tunneling?). The protons and neutrons are made up of quarks, which are made up of strings, which, as far as we know now, are the smallest anything can be divided into. The distance between electrons is difficult to say because they are not fixed to one place at any one time. There is lots of "empty" space in between the various particles making up atoms. I say "empty" in quotes because empty space is teeming with virtual particles. I don't know the size of these virtual particles so maybe someone else will correct me here if I'm wrong, but these virtual particles make it impossible to say that there is truly empty space. If I was mistaken on anything here please correct me, hope this reply helped.

Thanks for the replies so far, they were very helpful. So is there a point of maximum compression? Or does the amount of energy required to further compress anything increase exponentially?

Gravity waves couldn't necessarily be used to make anti gravity. You could have two sources of gravity pulling in opposite directions, as schneibster said earlier, but this isn't really antigravity. You could try to make an interference pattern, as ydoaPs suggested, but this would only be possible if you had something that could block out some parts of the gravitational waves, and I suppose if you had a gravity blocking wall, then cutting holes in it to try and make anti gravity interference patterns would seem a bit odd. The only way I can think of to produce anti gravity is to warp space time and utilize the fact that gravity doesn't travel faster then light to make temporary spots of increased gravity forming interference patterns, these interference patterns might help a little but again, if you can warp space like this, do you really need anti gravity when you can just warp it to the point where it's almost gone? If I worded something bad or said something wrong please mention it.

Can water be compressed? I have heard multiple conflicting views on this. Assuming that you could compress water, could you compress it to a point where any further compression would not be possible? If so then could you make a tube, full of water, and push the water from one end and have the force traverse the length of the tube instantaneously? Compression waves can't happen in water, unless I'm mistaken. I'm more then a bit confused on this and wasn't entirely sure where to post this. I hope posting this here is alright, as it has to do with faster then light data sending and the physics of water.

I'm not sure if this will help, as other users have already said a lot about this topic that was very helpful. That being said, I think I can help answering the "what is pure matter?" question. Pure matter is not possible if you consider string theory. If all atoms are made if protons, neutrons, and electrons, and protons and neutrons are made of quarks which are made of strings, which are one dimensional, then all compression of empty space in the third dimension would prove to be pointless. It would take an infinite amount of one dimensional objects to make up any non-zero space in the third dimension. So therefore, all compressed mass must be due to the size of electrons. Compression of electrons would prove to be a very futile effort because their charges would repel each other. So the electromagnetic force would overcome gravity as the distance between them gets smaller and smaller. Gravity would get stronger, but electromagnetism would get much, much stronger. Though I suppose if you consider all matter to be standing waves then they can "interfere" with each other, though I wouldn't consider this compression. Hopefully this helps, if not, I can try to clarify more. Also, if something I said was wrong, please point it out.

Thanks, this was very helpful and informative. Id love to have a discussion, I don't know much about these errors/attacks but I'll give it a try anyway. What I was wondering is how these types of attacks can be detected. I understand you may block certain strings that can be mistaken as code by another machine using a different launage, but how can you tell, say, what IP adress sent out that specific request. And if the user/hacker were clever enough could they send a string to the server that would mask their IP? Or are some commands too powerful for any system to allow outside strings to influence. If this reply didn't make any sence at all then sorry, like I said I'm still pretty new to this.