It is possible for any sequence of numbers to be generated in physical reality, including a sequence of prime numbers. But choosing primes does reduce the possibility that we would just be seeing some kind of resonance, and thus increases the chance that it was sent by a conscious entity. The longer the sequence, and the larger the primes, the less likely that this would be produced by accident. Would it be evidence? Yes. Would it be proof? Not absolute, but as we currently understand the universe, it would be pretty convincing.

Prime numbers occur in nature exactly as frequently as you would expect from their position on the number line.

@keshlam Yeah, I was thinking resonances and harmonics. The spacing between pulses = spurious.

You cannot infer design until you can show that that very designer is more probable than even the most improbable of improbable things! It doesn’t matter how improbable the prime number sequence is. The designer’s very existence must be more probable for you to conclude that he exists. It doesn’t even serve as evidence, much less “proof”, until that is established.

@Syed Well, this question wasn't about about evolution, but I will say that it's a matter of opinion. If you see a watch on the beach, obviously it was designed—by humans, but it was obviously designed on purpose. == Some people think that the complexity of humans vastly exceeds the complexity of a watch, and that natural selection does a horrible job of explaining all this. I feel embarrassed for people who try to explain it away.

@MissUnderstands you make that deduction because you already know humans exist. There’s no need to think about the probability of humans existing. It’s trivially 1. Probability is a function of uncertainty. We don’t know if other designers exist, and frankly, they seem much more improbable than a long sequence of prime numbers, especially a god!

@Syed I'm not trying to estimate the probability of humans existing! And I don't have to estimate the probability of a designer to observe that animals appear to be designed. All their parts have purpose.

@MissUnderstands And the proposed designer would also have functions that would seem purposeful. So why posit a designer?

@MissUnderstands What is the purpose of the blind spot in mammalian eyes?

"He did that because supposedly, prime numbers do not occur in nature." That's fiction, not philosophy. "William Dembski, ID advocate, also asserts that receiving a sequence of prime numbers of clicks by radio would be de facto evidence of life." No he does not, and you did not cite him doing so. He cites an illustrating example from a hollywood movie, not as argment, just as illustration.

@keshlam I'm not sure what that means. A particular prime number cannot be generated by a periodic processes with a period anything other than the prime number itself. If we assume that some natural processes are aperiodic, and that others are periodic with periods not tied to prime numbers, you would expect to find prime numbers less often, since all of those periodic processes almost never generate prime numbers (at best, exactly once, followed by an arbitrary number of non-primes).

What distinction does de facto make here? What sort of evidence would not be de facto?

@nuclearhogie: The Law of Small Numbers means that most of the numbers we see are smaller ones. Primes generally become less common as the range of numbers increases. You would expect 3 or 5 to occur about as frequently as 2,4,and 6, and 1500450271 to occur about as frequently as 1500450270 and 1500450272 ... but as the number of digits increases the odds of a random choice being a prime decrease. If I saw the sequence 5915587277, 1500450271, 3267000013, I would be FAR more certain that there was someone sending it than if I saw 3,5,7,11.

@MissUnderstands "If somebody leaves a note on your door, you can infer that someone left a note on your door." How and why can you infer that? Why "someone" and not "something"? I think you can only infer that it is someone if you use you experience that other people exist, that people sometimes leave notes, etc. In the fall, thousands of leaves are blown by the wind and land near my door. If I find a particularly nice and complex looking leaf next to my door, should I infer someone left it there on purpose?

@Philomath > What is the purpose of the blind spot in mammalian eyes? == The fovea. I believe it's a place where all the nerves from the retina penetrate the eyeball. Is that correct? What do I win?

@NuclearHoagie > s. A particular prime number cannot be generated by a periodic processes with a period anything other than the prime number itself. == Correct! So doesn't it follow that a stream of nothing but prime numbers is indicative of intelligence?

@MissUnderstands I thought you were intelligent enough to get the hint. Just pointing out poor design. If you're willing to believe that a Designer can design something as mindboggling complex as a human being, then how come she doesn't have the insight to connect the optical nerve to the other side of the retina. Not that she doesn't know how to do this, because the octopus has a better designed eye: no blindspot. Or might it be convergent evolution?

@Philomath You're not gonna get out of this by micromanaging And second Guessing the choices that the creators made. == Or might it be convergent evolution? == It might be in but it looks to me like intelligent design.

@MissUnderstands "Is that correct?" - No, that is not correct.

I don't think the title of this question matches what you are asking. "Do prime numbers occur in nature?" Yes, if you think ideas in human brains (and/or other animal brains) are part of nature. If not, no, because numbers in general only exist in minds. If we ignore that and just assume that things we can count are part of nature, you are surely aware of flowers and starfish. Maybe you mean "are prime number sequences found in natural phenomena?" or something to that effect.

@JimmyJames > Maybe you mean "are prime number sequences found in natural phenomena?" == no, I mean what I said. == > I don't think the title of this question matches what you are asking. == then change it If you believe my question should be a different question. Change it all around. Do anything you want . I won't complain.