Two Stanford University mathematicians found that the ending digits of prime numbers are actually less likely to repeat in the next prime number.
Prime numbers may not be as random as mathematicians previously thought –– a discovery that could eventually have real effects in fields like cryptography or cybersecurity.
A quick math refresher: Prime numbers can only be divided by one and themselves. Two and five are examples.
Start listing primes, though, and once you get past two and five, you'll see that if a number is prime, it will end in the digits 1, 3, 7 or 9.
Scientists thought those four ending digits were random and had an equal chance of being the last digit of a prime number.
But two Stanford mathematicians found it's not so random after all. For some reason, when analyzing the first billion prime numbers, the ending digits didn't have an equal chance of repeating themselves in the next prime number as the other three digits, making one digit easier to predict than the others.
So for example, a prime number ending in 1 is less likely to be followed by another prime number ending in 1.
Their work still needs to be peer-reviewed, but one of the researchers told Nature, "Every single person we've told this ends up writing their own computer program to check it for themselves."
Now back to cryptography. When you purchase something online, prime numbers keep your card number safe. They've been used because their seemingly random nature made them hard to decode.
Quartz reports, for now, the Stanford mathematicians' discovery doesn't change or endanger our financial security. But the researchers admit there's a lot they still don't know about their new phenomenon, and as they learn more, cryptography rules might be forced to change.
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prime numbers are not random, they follow a very nice equation. I came up with one with is a infinite series, it will always tell you if a number is prime... if they were random we would not be able to come up with an equation.
Эти два математика из Стендфорда cделали не верный умозаключение.
Метод меньших квадратов Гаусса тоже не выявляет функцию Хаоса. Гаусс нашёл - Ln, однако прозевал RND-i.
Очевидно, что обыкновенные числа являются полностью случайными. Да, они могут быть
вычислены. Природа обычных чисел двояка, будто у простых частиц, которые в одном
случае могут владеть волновые характеристики, а в другом владеть характеристики частиц.
Тут главную роль играет - ИНФОРМАЦИЯ.
These two mathematics from Stendforda University is not the correct conclusion.
The method of least squares Gaussian also reveals no function RND-ideal. Gauss found - Ln, but missed the RND-i.
Obviously, the prime numbers are completely random. Yes, they can be calculated.
The nature prime numbers of duality, for elementary particles, which in one
event may have a wave properties, the other properties of the particles have a.
Here plays a major role - INFORMATION.
I think you're confusing what I've said with some more all-encompassing result; I have stated no error.
All the same, nothing I've stated can answer the challenge of the Riemann Hypothesis; yet the obvious fact remains that (individual) primes *can* be determined by computation.
When sufficiently large, and not members of certain special classes (such as Mersenne or Fermat), computation becomes impractical/physically impossible; but computability is a much more lenient requirement, which ignores practicality.
Of course there remain many unanswered questions about their distribution; the existence of a formula that produces infinitely many distinct primes; the ability to produce the n'th prime by closed formula; proof/disproof of the infinitude of twin primes; etc.; are all unresolved.
And same goes for the Riemann Hypothesis.
Is this clear enough, or do you need further explanation?
Being able to determine whether a number is prime or not isn't the same as predicting which number next will be prime or not. Yes, we can through computation determine whether or not 15 is prime or not. We can try to divide it by 3,5,7,11. Hey, it is divisible by 3 and 5. It is not prime. This is a trial and error method. What if we wanted to know "What number is the ( n )th prime out of all primes?" So, tell me what is the ... 152th prime number? All of this is done through trial and error computation. Because they appear to be random. There seems to be no predicatable way to determine primes.
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