Random Sequencer?

If it were possible to create a random number sequence generator, would it be any more likely that it would generate whole number sequences rather than prime number sequences?

1,2,3,4.... vs. 2,3,5,7.... same probability?

Update:

thanks for the help. i understand its nonsensical, thats why i said "if it were possible." the first answer is correct. and you're right i forgot to specify that i meant whole numbers. anyway, i'd like to change the question to : if we were sending "blips" of numbers into space to show intelligence, why send a sequence of primes instead of any other sequence?

Relevance

It's not really clear what you're asking. From what set of numbers is the generator drawing--all real numbers? All rational numbers? All natural numbers? With what probability distribution?

One part of the incoherence of the question here is that you cannot draw with uniform probability over an infinite set. Thus, it doesn't really make sense (without a particular probability density function in mind) to talk about "random sequences of numbers."

This leads to a number of conflicting answers. If the sequences are of real numbers, then, assuming your PDF doesn't favor whole numbers, the probability will be 0 of getting any sequence of whole numbers--or even hitting a single whole number in a given sequence, or even hitting a RATIONAL number in a given sequence. Thus, the probabilities would be equal and both 0.

On the other hand, the average space between primes does get large as the numbers get large (it grows roughly logarithmically). Thus, it is in some other sense *less* likely to come up with primes than with whole numbers.

Again, this really depends on what you mean by a "random number sequence generator." The term is, in the usual interpretation, nonsensical, and so the question is, without further elaboration, ultimately nonsensical.

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** FOLLOW-UP: **

"If it were possible for a number to be both odd and even, what is the probability of a randomly selected rational from (0,1) having a numerator in reduced form that is both odd and even?"

That makes about as much sense.

Logic 101: If the hypothesis is false, ANY inference is true. So, yeah, the probabilities are equal; they're also not equal. It's 0% likely that you get all primes; it's also 100% likely that you get all primes.

As to why we send out strings of primes... Because the strings AREN'T random. They're strings of consecutive primes. Could we send out strings of consecutive numbers and have it be equally non-random? Sure. But I suppose sending primes tells *slightly* more about our development than sending out strings of consecutive numbers.

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