Prime Definition and 756 Threads

The GIMPS project is aimed to search (and find !) new Mersenne prime numbers. It has just discovered a new huge prime number, named M42, which has been verified with a different software on a different computer architecture (a third verification is on the way). It is the 8th Mersenne prime...

Prime Number Importance??Help Please What is the importance of finding away to descirbe prime numbers in relation to both themselves as well as other numbers? :rolleyes:

I've been going over this on paper for a while now, so I was wondering if maybe you guys would be able to point me in the right direction. We're supposed to prove that if every even natural number greater than 2 is the sum of two primes, than every odd number greater than 5 is the sum of 3...

In countries where they have both Prime Ministers and Presidents, WHAT ARE THE DIFFERENCES BETWEEN THEM?! Thank you, Jacob

Are prime numbers more than a curiosity? I know they can be useful in encrypting data but do they have a more fundamental role in the physical world? For example,a prime number won't split into two equal integer numbers. Integers occur in quantum mechanics - our most fundamental description of...

The RSA encryption algorithm that makes use of public keys, is widely used in secure communications such as e-commerce. It depends on the fact that you can multiply two very big prime numbers to get a product, but someone else cannot get back those prime numbers (factorize the product) directly...

So is it? Something I have been thinking about lately.

Ok, I posted this in the software forum a this afternoon, but I guess all the java gurus are on vacation. So I thought I'd post it here. This is my problem: Ok, I have a new problem. This time I'm trying to make a program that prints all the prime factors of a given number and the 29...

Hey, A while ago i hear about finding the division number theory [Tell how a number can be divied be another unmber as a general formula]. And i am wondering if there is a theory "desicovered" the pattern of the prime numbers. Or at least a fixed pattern for predicting some of the prime numbers...

Is there a method one can use to obtain the prime factorization of a certain number? For example: Find the prime factorization of 49 + 39. [MathFest 2004] I realize that I can re-write the expression as 29.29+39, but that's about as far as I can go. :cry:

Hello all. I know there is a stupidly easy algorithm to find the prime decompision of a number (i.e. 2*2*2*3*5 is the p.d. of 120) but I can't for the life of me remember it. I need to do this operation on incredibly large numbers (~500 digits) so the naieve way of just starting at 2 and...

Hello all, I am currently writing a program where I need to find a generator in VERY large modular prime systems, where p can be anywhere up to 2^1024. Is there an efficent (i.e. hopefully polynomial time on the number of bits) way to do this? For example, the current system I am working in is...

i don't even know where to start and i hate series. if someone could get me stared that would be great help. thanks The terms of this series are reciprocals of positive integers whose only prime factors are 2s and 3s: 1+1/2+1/3+1/4+1/6+1/8+1/9+1/12+... Show that this series converges...

I was reading this tutorial and I came across this part which I didn't quite understand: I don't follow this. What does "a will be counted j times and will contribute i towards t" mean? Why does this show that t=s?

Hi everyone, This is a simple question which has probably already been solved by someone, but I couldn't find it in the research anywhere, so maybe somebody here can help. First of all, say we have a program which uses a new algorithm that outputs the nth prime when you input n, I call it...

P corresponds to prime digits(i donno what thi means...i am giving exactly as given in a test) 7P5 x33 --------- PPPP PPPP ---------- PPPPP Find the value of P?

What is the y prime of: A 15 foot board rests against a vertical wall. If the bottom of the board slides away from the wall at the rate of 3 feet per second, how fast is the area of the triangle formed by the board, the wall and the ground changing at the instant the bottom of the board is 9...

is it true that for any set S:={1,...,n} 2*p>n , where p is the largest prime in S? Thanks in advance :biggrin:

We didn't talk about prime numbers in my class, but several of the homework problems mention them. For instance: Prove that if every even natural number greater than 2 is the sum of two primes, then every odd natural number greater than 5 is the sume of three primes. Assume that n is an...

A man called du Sautoy proclaimed in a book that some superdigit primes are unique, hard to calculate and probably have some sort of special underlying pattern. All I can tell is that a prime is the difference between two consecutive squares. What have YOU come up with?

im making an algorithm in which i need to generate two 1024 bit prime numbers, is there a way of doing this? i read that there are some ways to see how probable it is that a number is prime, can you guys point me in the right direction?

is it true that this function: f(n) = 3^(n)+2 will give a prime number for any natural value of n?

I am trying to find the best algorithm that will find the prime numbers just for fun.. I am not a programmer so let's talk here in english please.. For example ; - For the algorithm to run faster it must not calculate even numbers. a = 1 a = a + 2 the number that will be searched...

When trying to determine whether a number is prime or not, the following algorithm is often used: Test all numbers up to [sqrt[n]] ([x] is the ceiling of x) to see if any divide evenly into n. If any do, the number is not prime. My question is, why do you only have to test up to [sqrt[n]]...

I'm sorry if this is a stupid question, it certainly seems like someone must have have thought of it before. Anyway, here it is: is -1 a prime number? After all, primes are divisible only by the number 1 and by themselves. -1 is divisible only by 1 and itself. Is it therefore the smallest...

Starting at 10, for any set of 5 consecutive odd numbers, at most 4 can be prime (the number ending in 5 cannot be prime). Moreover any such set has to have the number ending in 5 as the middle of two pairs of prime (you cannot have 3 consecutive odd primes when you start after 10). The first...

The Liberals have a huge lead this election in Canada. You can watch it on CBC. So, who do you want head of Canada?

Here is a tentative conjecture that needs to be tested. [P! + P]/P^2 = INTEGER if and only if P is a prime number P! is P factorial, e.g. 3*2*1 , 5*4*3*2*1 , 7*6*5*4*3*2*1, etc...

Would someone PLEASE help me. This is very basic, so I know this will be simple to you guys. I need to know how to break a random composite number down into its simplest prime form. Like 4=2 squared. Or like 12=3*2. I need to know how to make up larger composite numbers out of their most...

http://www.newscientist.com/news/news.jsp?id=ns99995057 The time it took to calculate? 14 days, the reward? $100,000 now the wait is on for a 10-/100-million/1-billion digit prime number :eek:

Nommos Prime (Dogon) "Getting Too Close...?" From; http://www.marstoday.com/viewnews.html?id=954 “Notwithstanding that Mars is a very harsh mistress--missions fail with rueful frequency --it is now clear the cards were more heavily stacked than usual against the diminutive Beagle 2, and...

Nommos Prime (Dogon) Gets "Another One Right On (or "UP") The Nose" Well, thanks to the most diligent (and rather covert, perhaps even illegal) tracking by me, Muster Mark (3) and especially Sven, it has been determined that Mars Express has “passed over” the Face on 3 separate periapsis...

Hi, Let's talk about Prime Numbers. Still an unsolved mystery, I don't understand why it's still unsolved. Has anyone discovered why its hard to find a pattern? Or is this a silly question?

Such as sqrt 5: (2.236067977...) Start with the fractional seeds 2/1, 9/4,... New members are generated (both numerators and denominators) by the rule new member = 4 times the current plus the previous. Which generates the progrssion 2/1, 9/4, 38/17, 161/72, 682/305, 2889/1292...

Here is a cool article about a pattern to the procession of prime numbers: http://www.nature.com/nsu/030317/030317-13.html Enjoy! :smile:

Is there any good reason to define 1 as a non-prime number?

I was told that all prime numbers (except 2 and 3) could be expressed as 6n +- 1 as long as the result divided by 5 is not another integer. Is this true? Is there a proof for this (hopefully if possible not going much beyond basic calc, I am only in calc 1).

M^2 is your answer. Where M = largest known prime :-)

How can I prove that the sum of two odd primes will never result in a prime? Would this be proof?: Proof by contradiction: The sum of two odd primes will sometimes result in a prime. This is true because 2 + 3 = 5, which is a prime. So since this is true, does this proof the...

I have to prove that if ab is divisible by the prime p, and a is not divisible by p, then b is divisible by p. In order to prove this, I have to show (a,p)=1. I am not sure what this statement means. Then I am supposed to use the fact that 1=sa + tp when s,t are elements of the set of...

I've heard ppl say it is and it isn't, so is it a prime number? :P

Has anyone ever tried to make prime numbers into some kind of geometric equivalence? Such that prime numbers can be predicted through geometry? I was thinking of a universe beginning with one 3D unit, and evolving from that unit. That all subsequent units would have a relation to the first...

Does it make sense to Fourier-analyse pi(n) for finding patterns toward a comprehensive prime-predictive formula?

Hey, check this out, the newest prime number found today! http://story.news.yahoo.com/news?tmpl=story&cid=528&ncid=528&e=10&u=/ap/20031211/ap_on_hi_te/biggest_prime_number

This is strange... I can sort of proove this. ( n(1/2 + 1/3 + ... + 1/pa) - (1/3 + 2/5 + ... + (a-1)/pa) minus all whole queries ) <= ½ --> n = p If it's true and I was the first to find the serie; can I name it after me? In that case i would like to name my equation the...

Yes, ofcourse, a primenumber is a number that can only be divided with itself and 1. But what do you call a query that has only got two different prime factors? 9 has got the factors 9, 3 and 1. But has only two different prime factors. 9 = 3*3, so the query has got the prime factors 3 and...

Consider all primes 2, 3, 5, 7, 11, 13... and their products such that 2x3=6, 2x3x5=30, 2x3x5x7=210, 2x3x5x7x11=2310, 2x3x5x7x11x13=30030... Is this latter series used in number theory? Likewise, can one determine lim (2+3+5+7+11+13...pn-1)/(2+3+5+7+11+13...pn) n-->[oo]...

I've been Googleing for days now and haven't found a suitable answer to a question I have so I'll try it here. How exactly would knowing the distribution of prime numbers assist one in integer factorization?

Determine the ones place value of the product of the first 1000 prime numbers.

Hi everyone, I'm new here. I have an interesting conjecture I have been trying to prove for some time. I've tried it out on a couple of forums, but perhaps some of you can help. Please make whatever comments you can (good or bad) and all input is welcome. I will give this conjecture in...