Prime Definition and 777 Threads

The prime ministers A, B, C, D, E, F and G of 7 countries will address at a summer meeting. a) Find the number of arrangerments that can be made so that 1)A will speak before C, 2)A will speak before C and C will speak before E. b)In how many of those ways in a2) will C speak immediately...

A formula of prime numbers for interval (q; (q+1)^2), where q is prime number. Let: Q_k – the multitude of first k prime numbers to some extent: Q_k = (q_0 = 1^0, q_1 = 2^n1, q_2 = 3^n2, q_3 = 5^n3, q_4 = 7^n4, … q_k = u^nk) (here the expression «_i» signifies lower index, and «^ni»...

I saw a proof saying the root of a prime is always irrational, and it went something like this: sqrt(r) = p/q where p/q is reduced r = p^2/q^2 r*q^2 = p^2 therefore, r divides p so define p = c*r r*q^2 = (c*r)^2 = c^2*r^2 q^2 = c^2*r therefore, r divides q also since r divides p...

Hey there, I've been having some problems trying to prove this: "Let p be an integer other than 0, +/- 1 with this property: Whenever b and c are integers such that p | bc, then p | b or p | c. Prove p is prime. [Hint: If d is a divisor of p, say p = dt, then p | d or p | t. Show that this...

Where can I find examples, or a complete list, of computer generated (common prime factor) solutions to the Beal conjecture problem?

Is this equaltiy exact?: \Pi(a_p+b_p)= \Pi(a_p)+\Pi(b_p) where both products a_p,b_p and (a_p+b_p) converge another qeustion \Pi 1=1 ? all products are made respect to all primes..

I found this on arxiv...is this guy a loon or do the proofs seem reasonable? Proofs

Hi! How do I determine the number of distinct factors of a number, say, 2520? 2520 = 2*2*2*3*3*5*7 So we've 8 different primes. The number of combinations of those is, according to me: C(8,1)+C(8,2)+...+C(8,8)=155 (I think, calculated it by hand; but it isn't important) Obviously those...

Why is 1 not considered a prime number? It meets the requirement of being only divisible by itself and 1.

Curious about this pattern. list(6N,-1,+1)less list((6n,-1,+1)*(6N,-1,+1)) produces 100% primes =>5 for as far as I am able to take it. Sorry the dwgs would not copy so have added attachments. This pattern of products repeats by value (first digit set, second digit set, etc) and by...

We all know the definition of prime numbers and the first prime number is always 2. Why is -1 not listed as a prime number? , it qualifies as it passes all tests for a prime number.

Investigating the Diophantine equation q = \frac{n^2+1}{p}} where {p} is a prime number, n,q are integers per definition The prime numbers can be sorted into two groups Group 1 has no solution and Group 2 has the solution n = \{ a\times p - b{ \ },{ \ } a\times p + b \} {\ \ \...

Why is it so difficult to predict prime numbers? And has Riemann's conjecture been solved yet?

I am wondering about the general definition of relatively prime in terms of commutative rings. Specifically if I have my first definition being that given a commutative ring R if r_1 and r_2 are relatively prime then if r_1 k\in r_2R then k \in r_2 R. And vice versa. In other words if r_2...

Hi, I am trying to prove that if o(a) and o(b) are relatively prime, and ab = ba, then o(ab) = o(a)o(b). I'd appreciate it if someone could give me a nudge in the right direction because I've spent almost 2 days on this now and I got nowhere. Which is rather annoying considering this is the...

There is (as far as I know) no proof-for or against- that there are infinately many prime pairs such as 3, 5 or 29, 31... Anyway, is it intuitive to assume that there should be infinitely many pairs just b/c of the fact that there are infinitely many numbers? or does this have nothing to do...

So I just heard about the new prime number that was discovered and for some reason got kind of interested in it. So I'm looking at prime number tables on various webpages that show the prime numbers, dates discovered, etc. I'm confused on what the "digits" column in these tables means...

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?

Hello, i have developed a formula for inverting a dirichlet series ,and i apply to solve Phi(n),Mu(n) and d(n) arithmetical function,also i give a formula to obtain the Pi(n) function by means of a triple integral, the paper is in .doc format but if someone want to see it in .pdf can go to...

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...

in this postcrpit i would like to say i have fund a second order integral equation (fredholm type) for the prime number counting function in particular for Pi(2^t)/2^2t function being Pi(t) the prime number counting function,teh equation is like this is we call Pi(2^t)/2^2t=g(t) then we have...

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...