Friday, July 29, 2016



Consider primes and only 1 and themselves factors on them, and you must understand that the higher the number, the less likely that it will be, because prime is less than more and more numbers than this may be his factors.

 It turns out that the most important factor for any number can only be as big as its square root, for reasons which I will not discuss here, but let's take a number like 13, its possible factors may be only 2, 3 and 5. Of course, we already we know, there are no factors of 13, but if we look at the larger number as 329, we get a slightly different story.

 I can not tell you if it's a prime number without checking himself, but that is not the point here. I know that it can have all the same factors as the 13, but many more of them, and maybe even including him. Factors 229 can be 2, 3, 5, 7, 11, 13, 17, 19 ... and further upwards.

 What I'm trying to show here that the greater the number, the more factors it could potentially have, and will, therefore, less likely, it would not have a single one.

This happens to be true, but you might suspect that as soon as the number becomes large enough, it simply can not be, perhaps, the prime of all these factors, which could make it.

 It's impossible to tell for sure if a simple end just because we continue to find them, but the mathematics are confident that no matter how large the number, simply continue to exist, although less and less.

 So a number of trillions and trillions of digits and there is still the Prime Minister. There is a formula that gives us a rough estimate of how many there are a number of simple concrete number that is equal to Ln (N).

 So, if you want to see how often you can expect to see a certain number of simple close, just paste it into your calculator.

First, let's look at how a small number 501. Ln (501) = 6.2. So about one out of every 6 prime numbers close to 501.

 Now let's look at Ln (10 ^ 500) = 1153.6. Here's where it gets weird. Roughly 1 in every 1100 numbers with 501 digits prime, that is, he has no other than himself and one of factors.

 I trust the math, but it's hard to imagine that the figures, which could no longer any factors at all, but no matter how great your prime number in the list, each number on it there will be no factors! This also applies to the prime factors of answering the question, what is the prime factors? because each room is simple factor, even if only one of them and himself.
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