Prime Definition and 756 Threads

I bumped into this problem on the net, and the question is as follows: How would you go on to solve this? Here are the solutions for the given equation: p = \frac{-x^2}{x-444} x = (-p \pm\sqrt{p^2+1776p})/2 Remember x must be an integer, so there must be an integer q = np+m and...

Some time ago I began playing around with packing circles and I have some questions that I am hoping someone here can help with. I have linked to three PDF files that should help in understanding my synopsis below. (You will need to click on the blank sheet and then open the PDF’s as I am...

1. THERE EXISTS AT LEAST TWO PRIMES NUMBERS BETWEEN N^2 AND (N+1)^2, WHERE N IS A NATURAL NUMBER. 2. THERE EXISTS AT LEAST ONE TWIN-PRIME PAIR BETWEEN N^2 AND (N+2)^2, WHERE N IS AN ODD NATURAL NUMBER. (THEREFORE THE TWIN PRIME CONJECTURE IS TRUE) anyone will a powerful system can verify...

Homework Statement If F is a finite field show that there is a prime p s.t. (p times)a+a+...+a=0 for all a in the field Homework Equations The Attempt at a Solution Well I managed to prove that there must be an a in F s.t. (prime number, call p, times)a+a+...+a=0 but I can't seem...

Ok, well a corollary to Lagrange's theorem is that every group of prime order, call it G, must be cyclic. Consider the cyclic subgroup of G generated by a (a not equal to e), the order of the subgroup must divide the order of p, since the only number less than or equal to p that divides p is p...

Homework Statement Let H be a normal subgroup of prime order p in a finite group G. Suppose that p is the smallest prime dividing |G|. Prove that H is in the center Z(G). Homework Equations the Class Equation? Sylow theorems are in the next section, so presumably this is to be done without...

Find all prime numbers (p,q,r), that numbers pq+pr+rq and p^3+q^3+r^3-2pqr are divided by p+q+r

My quantum professor, as an aside challenge, asked us if we could write a program in Matlab to factorize a 32 digit number into its prime number constituents. Can anyone direct me in the right direction to research how to do this? thanks, Greg

I am doing a homework assignment for my philosophy class. He wants us to do a simple assignment that verifies the proof that there is no largest prime number. He claims it has to be where someone states to me "there is a largest prime number" I would say that is not true it is infinity and here...

Suppose you divide all non-prime numbers in two categories, those which (a) have a prime factor greater than the square root of the number, and those which (b) don't, and all prime factors are less or equal than the square root. Let Ca and Cb be the count of numbers in categories (a) and (b)...

Homework Statement find the derivative of... 2 sinxcosy = 1 The Attempt at a Solution (2 cosxcosy) * (cosy') cos y' = -2 cosxcosy y' = (-2 cosxcosy)/(cos) I know that's not right but I am not sure where I am making the mistake.

Homework Statement I'm starting an introductory course in "Advanced math" and need a little homework guidance please. The question: Let a, b, and q be natural numbers, and q > 1. Prove that if q has the property: q divides a or q divides b whenever q divides ab, then q is prime...

I was wondering if any nontrivial bounds for http://www.research.att.com/~njas/sequences/A008407 were known. This is the sequence of minimal width for k-tuplets of primes allowed by divisibility concerns. a(2) = 2 since n, n+2 could both be prime; n, n+1 isn't admissible since then either n...

Hello, This is my first post. Anyways, from the beginning, since I started learning the subjects at higher level, I have faced this problem - How to determine if the nos. is a prime no. ? The numbers under 100 are known to me, but if a bigger digit comes, are there any tricks to...

twin prime acceleration! few weeks ago while i was doing my physics homework, i thought about the acceleration of prime number, so used the kinematics equations of acceleration on prime numbers. i was amazed to find that the difference of square of two prime numbers(>5) are always divisible by...

This is for a proof but I was generally more curious so it isn't in the homework section. If I were to make a set A which is defined as all the prime factors of an integer a there could be some numbers in A which are repeated, would these count as distinct members or not? The reason why I was...

I posted the following on my blog (http://fooledbyprimes.blogspot.com/2007/07/silly-primes.html) Not until recently has the whole prime number "culture" become a distraction to me. While a child the primes never really caught my attention. Even in college there was not much drawing me to...

Homework Statement I was able to prove both of these statements after getting some help from another website, but I am trying to find another way to prove them. Can you guys check my work and help me find another way to prove these, if possible? Thanks. Part A: Show that if 2^n - 1 is...

Double check -- this is prime, yes? I thought I had uncovered some kind of pseudoprime, since I found this number with pfgw and on checking it, found it to be composite. I tested it for pseudoprimality with a battery of tests, though, and it passed all of them -- leading me to think that I was...

Well i read this somewhere that most prime numbers will give a whole number when equated with the formulae 6n+/-1(plus or minus) Is there any proof for this or is it just a coincidence.

Hi I was playing around with ways to store numbers more compactly in bases other than 2 and, just for giggles, I tried a "base" of consecutive positive integers that add up to "n". When I applied it to primes, like so • 2 = 2 1 2 = 3 • 2 3 = 5 1 2 • 4 = 7 1 2 3 • 5 = 11 1 • 3 4 5 = 13 1 2 3 •...

How would I write a program that finds all the prime numbers that are less than or equal to a "user-supplied" integer N, implementing the fact that I should only be dividing N by all prime numbers less than sqrt(N)?

Homework Statement Prove that for every k >= 2 there exists a number with precisely k divisors. I know the solution, but don't fully understand it, here it is; Consider any prime p. Let n = p^(k-1). An integer divides n if and only if it has the form p^i where 0<= i <= (k-1). There...

I was told by a math teacher I met recently that there is a formula that a mathematician in the 1800's came up with that accurately predicted all of the primes up to a certain point, but after that point began to miss a few primes, and after awhile, wasn't useful at all. Does anyone have any...

This was taken from a math contest a few months ago. Homework Statement xx*yy=zz find z if: x=28 * 38 y=212 * 36 Homework Equations Theres undoubtably some trick, but I have yet to find it The Attempt at a Solution Dont even think about calculator I showed my math teacher, and...

How do I find out if 4^2007 + 2007^4 is a prime number or not?

I have to prove that there excist an infinite number of prime numbers In that proof I apply that: n=p!+1 (where p is a prime number) this number (n) is not divisible with any prime number less than or equal to p. Why is that? Is there anyone who could please explain this to me or maybe...

Homework Statement Find the lim inf of p_n/n where p_n is the nth prime.Homework Equations Well p_n ~ n logn, but I'm not sure if a simple substitution would work. This question may be incredibly trivial or open, and I can't figure out which. I'm also wondering if the sequence above is...

1. Suppose that a and b are positive integers. Show that the following are equivalent: 1) a and b are relatively prime 2) a+b and b are relatively prime 3) a and a+b are relatively prime. 2. I know that for a and b to be relatively prime, (a,b) = 1 (that is, their greatest common divisor...

1. Here is the problem I'm stuck on: Let q be a positive integer, q is greater than or equal to 2, let a and b be integers such that if q divides ab, then q divides a or q divides b. Show that q is a prime number. 2. I know that q is prime if and only if 1 divides q and q divides q...

Consider the series with ascending (but not necessarily sequential) primes pn, 1/p1+1/p2+1/p3+ . . . +1/pN=1, as N approaches infinity. Determine the pn that most rapidly converge (minimize the terms in) this series. That set of primes I call the "Booda set."

[SOLVED] A different approach to prime numbers i read something about choosing a finite set of numbers as primes and deriving the other numbers from aforementioned set so that every number is obtained by multiplying primes (the numbers you choose to be prime in your system) in every possible...

Why is the characteristic of a finite field a prime number?!

Homework Statement Prove that if a prime p|2^{2^n}+1 then p=2^{n+1}k+1 for some k. Don't know how. I'm guessing by induction, perhaps?

Why does the eta prime meson have such a narrow decay width (ie long lifetime) compared to the rho and omega mesons? Is there some conservation rule that supresses its decays?

I think I read this somewhere, but I'm not sure it's right: is there a real number A such that Floor[A^(3^x)] is prime for all x?

I've written an algorithm that has the following goal: finding all prime numbers up to a specified integer. I've made two different algorithms actually: on one hand, I've used the concept beyond the ancient sieve of eratosthenes; on the other, I've used a function called isprime() that tests if...

Hello everyone. I think i got this right but i want to make sure... If p, q and r are prime numbers and a, b, and c are positive integers, how many possible divisors does p^a*p^b*r^c have? I said... There are a+1 divisors: 1, p, p^2...,p^a A divisor is a product of anyone of the a+1...

I was trying to do some heuristics with the Cramér model, but I wasn't able to find a good asymptotic for a certain quantity and I thought I'd see if anyone had something good. I did check a few sequences on the OEIS first, but I didn't notice anything there. Essentially, I'm looking to...

The question is: Show that if p == 1 mod 4, then (a/p) = (-a/p). (Note that == means congruent). I know that if X^2==a mod p (p is a prime) is solvable then a is a quadratic residue of p. For an example, I let p = 5 since 5==1 mod 4. Then, I let X = 2 and 4 just to check the equation...

Hi, I need help with this problem. Show that if a and m are relatively prime positive integers, then the inverse of a modulo m is unique modulo m. [hint: assume that there are 2 solutions b and c of the congruence ax==1(mod m). No need to prove that b==c (mod m) ] I have just started...

Theorem 1: Given a primorial p_n^{\sharp}>2, p_{n+1} is the second largest element in the reduced residue system modulo p_n^{\sharp}. Proof Clearly p_{n+1} is an element of the r.r.s. modulo p_n^{\sharp} since every prime less than p_{n+1} divides p_n^{\sharp}. Next notice that the...

I don't know if this is the right place to put this but it seemed close enough. Anyway I wanted to know if there was anyway to check whether a number is prime or not without doing a lot of division.

Hello everyone! I think i got this but I'm not sure if I'm allowed to do this. The question is: For all integers n, n^2-n+11 is a prime number. Well if that was a prime number it should be true that n^2-n+11 = (r)(s) then r = 1 or s = 1. But if you equate n^2-n+11 = 1, you get a...

Hi I have difficulty to begin with this problem: prove or disapprove that 2n-1 is prime for all non negative integers n. I know the definition of a prime number but how to apply it for this proof? Please, can I have a suggestion to start this problem? B

Hello everyone. I'm wondering if I'm allowed to use a counter example to disprove this. I'm not sure if I'm understanding the statement correctly though. THe directions are: Determine whether the statement is true or false. Justify your answer with a rpoof or a counterexample. Here is...

Hello everyone. I'm suppose to prove this but I'm having troubles figuring out how u find "distinct" integers. Meaning they can't be the same number. i figured it out they just wanted integers though. Here is the question: There are distinct integers m and n such that 1/m + 1/n is an...

Prime "spiral"?.. Sorry i don't know the name of this "Phenomenon" i heard (due to Sierpinski perhaps?) that if you distributed the prime numbers into an square in some manner there was an spiral that..run over all primes or something similar...i think it was called "Sierpinski spiral" or...

I am going through Hardy's book on number theory.The following theorem I do not understand. theorem 10: pi[x] >= loglog x where pi[x] is the prime counting function and >= stands for greater than or equal to The arguments written in the book are very compact.please help .

Can anyone tell me if Riemann's Prime Counting function can be solved by residue integration? Here it is: J(x)=\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\frac{ln(\zeta(s))x^s}{s}ds which has the solution: J(x)=li(x)-\sum_{\rho}li(x^\rho)-ln(2)+ \int_x^{\infty}\frac{dt}{t(t^2-1)ln(t)} I...