Prime Num Question

[Atlantic]

This may be a stupid question, but what numbers are prime and which aren't prime from -4 to +4

My friend and I are puzzled about 0 and 1.

It has been too long since we recalled.

 

thanks

[blike]

0 is not a prime number because it must be ONLY divisible by itself and 1. 0 is divisible by every number.

 

I don't know about 1, hopefully someone else can help there..

[jordan]

1 seems to fit all the rules for being a prime number. A search (on google) continualy says the definition of prime numbers includes only those greater than one, however. I'm not sure why, but 1 isn't prime.

[iglak]

i think a prime has to be divisible by only two different numbers (itself and 1).

1 is only divisible by one number... 1.

[wolfson]

The first ten prime numbers are:

 

2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

 

ONE (1) IS NOT A PRIME NUMBER NOR ZERO (0)

[YT2095]

agreed 1 is not a prime!

 

as for the -4 and +4 you may ignore the (+/-) and treat as normal.

 

and so your answer would be: -3, -2, +2 and +3

[jordan]

Can negatives be prime?

[YT2095]

of course they can, there`s no diference between "negatives" and "positive" numbers other than perspective.

Treat them the same

[jordan]

Why do lists of primes always begin with 2?

[blike]

In related news 2^20996011 - 1 is prime. Thats 6,320,430 digits long and is the largest known prime number.

[Dave]

I don't think negative numbers can be prime. If you take -2 for example, its divisors could be thought to be 1, -2 and 2, which would imply it not being prime.

[jordan]

blike, do you know how they test numbers like that.

 

dave, that is what I thought.

[alt_f13]

Hmm... 2/-2 = -1... -2/2 = -1

 

2/2=1 -2/-2=1

 

What if you walked upsidedown on the top of a frozen lake and went icefishing for ducks?

[wolfson]

Yes, there are negative prime numbers, but you don't have to worry about learning them. If you know the positive prime number, then you don't have far to go. The negative prime numbers are the opposites of the prime numbers.

 

The positive prime numbers start out with 2, 3, 5, 7, 11, 13, 17, 19, 23, etc.

 

The negative prime numbers start out with -2, -3, -5, -7, -11, -13, -17, -19, -23, etc.

 

I doubt that your teacher will even mention negative prime numbers to you. Most math text books don't even mention them.

[Dave]

wolfson: you should probably say where you got something from if you just lifted it from a website. (i.e. http://users.aol.com/AmazingMazeMan/primes/negative.html in this case). I'm not trying to be pedantic or anything, but it is part of our forum rules to give proper credit where due.

[wolfson]

Sorry one does apologise, I’m reasonably new, I don’t often quote from websites, I didn’t have time to comment personally on “negative prime number’s” but in the future I will wait till I have time.

[YT2095]

in that case I`ll credit my particularly Zealous maths teacher in college (If I could rem his name??)

so in regard to post #8 I`ll take the credit and share it 50/50 with my teacher, to your post #11

[jordan]

You said -2 is prime. This is because its factors are 1 and -2 (itself). We can't include -1 and 2, just like we don't say the factors of 5 are -5, -1, 1, and 5. Therefore it is prime.

Does that sound right?

 

Also, does anyone know how they test a number such as blike's 2^20996011 - 1 .

[YT2095]

It`s not a prime as it`s an even number by virtue of the 2^

I ignored the -1 bit for convenience LOL )

 

[wolfson]

Why would you want to test the number, would you like an equation?

[Dave]

jordan said in post #18 :

Also, does anyone know how they test a number such as blike's 2^20996011 - 1 .

 

A mixture of some very clever tricks and brute force.

[jordan]

Can you give me any more.

 

wolfson, you said there is an equation?

[wolfson]

That blike number is not a normal prime number it's the 40th Mersenne prime, Mersenne primes are realted by 2^p-1, and since there are only 40 Mersenne Primes then u won't be testing any of them at the moment, as for normal prime number, there is an equation it is quite long and highly defined, transposing the Nth term of the prime squenece would be eaier. I'll have to work hard and see if i can solve the Nth term.

[jordan]

Why are there only 40?

 

If the equation is really long, don't worry about finding and posting it. I was just currious whether it was an equation or some other method. I'm sure I'll run across it some day, though.

[wolfson]

OK by means of Mersenne Primes:

 

Mersenne Primes relate to exponent (e) or time ten to the power of x. The equation, is in relation to 2^n-1 is divisible by 2^n-1, when finding out whether a number (e) is a Mersenne prime we then have to use equation(s):

Since I have not fathomed out how to get my equation editor to work on scienceforums (due to my incompetence), you will have to bear with me:

 

So where was I oh yes equations to finalize correspondence between a number (e) and a Mersenne Prime:

 

Ok x and y are primes If y is divisible by Mx = 2x-1, then:

X = [+]/[-] –1 (mod8) and y = 2kp +1.

 

K being integer.

 

E.g. x =3 (mod4) be prime, then 2x +1 is also prime if it divides by Mx.

 

 

 

 

M(p) = 2p-1 and P(p) = 2^p-1(2^p-1) p is know to be a “perfect number” it has to be, to be a Mersenne. So divisible e numbers are:

 

2, 3, 5, 7, ….. until m12 (m= Mersenne), where perfect numbers are higher and much harder to solve, think of calculating all number 0 to 1.0x10^1666 (exclusion of 6), remember it must be divisible by Mx^ms, so well you would be there for ever, I know that they have computer programs for Mersenne Primes, but even that take forever, that is the reason for the ‘lack’ of Mersenne Primes. Although they are starting to be produced in a more increased dynamic, it will be a while for the 41st Mp I think around next year (maybe no hopes). I hope this helped explain the Mersenne number to you, if you have any more questions by all means ask away. And I haven’t forgotten about the equation for the normal primes hopefully tomorrow ill manage to crack that. And I’m also looking for triangle inside triangle pictures if anyone can get me them I would be very grateful (see post named FORMULA for more details).