Primenumbers

[Delphiki]

"Math can take a hike!"

 

[Lillen]

I did however say the product of two primes..

And also, I agree I was long time ago i bothered about math, i need to refresh my memory abit.

Explain to me why primes are so necessary in cryptation? The truth is that using other numbers always make you end up with atleast 2 answers (30 = 15*2 and 5*6)

 

[Upisoft]

I did however say the product of two primes..

Yeah, also known as "public key" in public/private encryption RSA.

 

[Lillen]

What most people focus on when primes is on the wall, is that it cannot be devided!

May i ask, can x^2 equation be used in simultaneously equations? I can only remeber cacluclting linear graphs when I read about simultaneously equations?

 

[Wiccan_Child]

What most people focus on when primes is on the wall, is that it cannot be devided!

Well, that's the only defining property of primes: that they cannot be divided into whole numbers by whole numbers, other than themselves and 1.

May i ask, can x^2 equation be used in simultaneously equations? I can only remeber cacluclting linear graphs when I read about simultaneously equations?

Simultaneous equations are equations which are simultaneously true (or assumed to be true). That means that:

3x + 4y = 5
2x + 6y = 10

As a pair of simultaneous equations, the values for x and y are the same in both equations.

That said, x[sup]2[/sup] isn't an equation.

 

[Freodin]

The truth is that using other numbers always make you end up with atleast 2 answers (30 = 15*2 and 5*6)

Again...

Every number can be written as the product of two or more prime numbers. This prime factorization is definite. There is only one.

In your example: 30 = 15*2 ... but 15= 5*3, so 30 = 2*3*5
same: 30=5*6 ... 6=2*3, so still 30 = 2*3*5

May i ask, can x^2 equation be used in simultaneously equations? I can only remeber cacluclting linear graphs when I read about simultaneously equations?

Yes, they can. Doesn´t make it easier to solve such equations though.

But I don´t understand what you are aiming at with that insistence on x^2. Neither in AV´s nor your system was there any variable squared.

 

[Chalnoth]

As for checking for prime numbers, except for a few special cases where you can prove a specific number is prime through other means, you need to verify a prime number by checking whether or not it is divisible by every prime number less than or equal to its square root.

So if we were to take the example of a 10-digit number and wanted to know whether or not it was prime, we'd have to check every number up to the square root of this 10-digit number (which is a 5-digit number). So if we wanted to know, say, if 99,999,999,997 was a prime number, we'd have check every prime number less than the square root of this, or 316,227.8. There are a lot of prime numbers less than or equal to 316,227. But it's not hard to write a computer program that will find prime numbers this large in relatively short order, if you desire to.

 

[AV1611VET]

So if we were to take the example of a 10-digit number and wanted to know whether or not it was prime, we'd have to check every number up to the square root of this 10-digit number (which is a 5-digit number).

Not.

Simply add 1, then divide by 6.

If that doesn't work, then subtract 1 and divide by 6.

If the quotient is an even number, then the dividend is prime.

QV please: 2

ETA: 99,999,999,997 is a prime number; as [99,999,999,997 - 1] / 6 = 16,666,666,666.

 

[Chalnoth]

Not.

Simply add 1, then divide by 6.

If that doesn't work, then subtract 1 and divide by 6.

If the quotient is an even number, then the dividend is prime.

QV please: 2

ETA: 99,999,999,997 is a prime number; as [99,999,999,997 - 1] / 6 = 16,666,666,666.

Works for some small numbers. Not for larger ones.

Take 41*31, for instance. 41*31 = 1271. Not a prime. And yet, if you add one and divide by six, you get an even number.

 

[AV1611VET]

Works for some small numbers. Not for larger ones.

Take 41*31, for instance. 41*31 = 1271. Not a prime. And yet, if you add one and divide by six, you get an even number.

Hmmm -- thanks for the wake-up!

(I'll have to tell the boys down at Mensa -- )

 

[Lillen]

Not.

Simply add 1, then divide by 6.

If that doesn't work, then subtract 1 and divide by 6.

If the quotient is an even number, then the dividend is prime.

QV please: 2

ETA: 99,999,999,997 is a prime number; as [99,999,999,997 - 1] / 6 = 16,666,666,666.

I am not worthy i am not worhty!

 

[Lillen]

As i've heard (an angel of ligth whispered it in my ear), you put the primes up to 1000 in a circle and put a pentagram inside. That will form the númber 666 using standard operations at the stars diffrent peaks in anyway you set the star.

The clock also cricles around the number 666.

This needs to be varified though, since that angel of ligth couldn've lie.

It is imortant to relized that we should be aware of the leaven of the pharisees and scribes. - Their teachings. There are people who end up in a wheelchair because they get stuck on primes. I have met a guy who needs two assistants while going to the bathroom. The same guy is fixated with primes. It can truly drive you mad or even kill you.



As a sidenote - Those people hatching ideas has been exposed to their leaven. Remeber delusions does not necessary need to be a lie, with delusions psychiatry means fixated ideas - you get fixated with some ideas. This is caused by pharisees and scribes leaven. As a DEA Agent trained by Uncle Fester, I was exposed to the mentioned leaven, their teachings. I almost blow up the lab in my youth (During the time i still was on drugs, nine years ago) as I almost created nitroglycerin instead of LSD. But illegal drugs and illegal explosives is not the only ideas you can hatch which you become fixated with. There are other ideas as well such as the pentgram and primes mentioned above which can cause paranoia as you see a dobberman pincher drive by your house!

 

[Chalnoth]

I am not worthy i am not worhty!

Actually, 99,999,999,997 = 17*5882352941. 5882352941 is a prime number, it turns out.

Just ran a quick computer program to verify (takes less than a tenth of a second to find all primes up to the square root of a number this size and check if it's prime, incidentally).

 

[Lillen]

Are you using bruteforce to do that??

 

[Chalnoth]

Are you using bruteforce to do that??

Yup, checks every prime up to the square root of the number to see if it's prime.

 

[Wiccan_Child]

Yup, checks every prime up to the square root of the number to see if it's prime.

Question: why do you only have to check up to the root of the number? I can see why you only have to go up to half the number, but the root? Madness.

 

[Chalnoth]

Question: why do you only have to check up to the root of the number? I can see why you only have to go up to half the number, but the root? Madness.

Hehe

Well, consider the possible situations:

1. Number has two factors, and they are the same. Thus, the prime factor is the square root.
2. Number has two or more factors, and one is larger than the square root. The others must, necessarily, be less than the square root.

Therefore, if the number is not prime, it will always have at least one prime factor that is less than or equal to the square root of the number.

 

[Lillen]

I don't follow you...

 

[Wiccan_Child]

Hehe

Well, consider the possible situations:

1. Number has two factors, and they are the same. Thus, the prime factor is the square root.
2. Number has two or more factors, and one is larger than the square root. The others must, necessarily, be less than the square root.

Therefore, if the number is not prime, it will always have at least one prime factor that is less than or equal to the square root of the number.

Hang on... Goldbach's conjecture... carry the one... bugger, you're right.

 

[Chalnoth]

I don't follow you...

Well, let's take an example.

Let's say we want to test whether or not the number 353 is prime. The square root of 353 is:
18.7882942

So, first of all, we now know that 353 isn't a perfect square.

But is it prime? Well, imagine, for the sake of argument, that there exists a number greater than the square root that is a root of 353, like 19. If this is the case, since 19 is greater than the square root, 353/19 must be less than the square root. So there isn't any need to check the number 19, we can just check the smaller number instead.

So we only need to verify whether or not the numbers 2, 3, 5, 7, 11, 17 divide into 353.

Turns out they don't, so 353 is prime.

Edit: to put this reasoning in equation form:

Suppose we have the following:

a*b = x

Here we are trying to find if the number "x" is a prime number. And we are giving it a guess number "a" which may or may not be a factor of "x". Now, let's suppose that "a" is larger than the square root:

a > sqrt(x)

We know that:
x/sqrt(x) = sqrt(x)

Which gives us:

x/a < sqrt(x)

Or:

b < sqrt(x)

Therefore, if one of the factors is greater than the square root of the number we are checking, then the other factor will always be smaller. So if we check for the smaller prime numbers, we don't need to worry about the larger ones. The smaller ones are enough.