Prime Definition and 777 Threads

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...

k-th "Twin prime"... Is not there a formula for the k-th "twin prime" ?..as far as i know for the normal primes satisfying "Wilson's theorem": (p-1)!+1=mod(p) you can get an "exact" (but difficul to compute) formula in the form: p_k = \sum_{n=2}^{2^{k}}(\frac{k}{1+\pi(n)})^{1/n} or...

is the square root of a prime number always going to be irrational? just a random question.

How is it that you calculate e and d such that ed=(p-1)(q-1)+1? Isn't this a factoring problem? How can you be sure that (p-1)(q-1)+1 is not prime?

We're really lucky to be living in a free country, no matter how flawed it may be. "BEIJING - D'oh! China has banished Homer Simpson, Pokemon and Mickey Mouse from prime time. Beginning Sept. 1, regulators have barred foreign cartoons from TV from 5 to 8 p.m. in an effort to protect China's...

can smby give me a simple example algorithm to determine whether the number is prime or not such as using while loop, if...then...else or others which is simple thanx

Are there any "prime gap" results like this ... I was just reading about "prime gaps" and noticed that most of the results are asymptotic, as in "true if n is sufficiently large". I was just wondering if there are any bounding results for prime gaps that are true for all n, p_n. For example...

Hello everyone, I'd first like to say that I am uninformed on this subject and that I have a question to the mathematicians on these forums who know about the subject. In the set of all prime numbers, has the integer gaps between two prime numbers been studied? I mean, do mathematicans...

I am curious as to whether this pattern will always hold true: Let's say we take the prime numbers: 2,3,5,7,11,13,17,19,23...primes and we take the square(individually) minus 1 3,8,24,48,120,168,288,360,528...p^2 - 1 Then starting with the third p^2 - 1 (24), all of the p^2 - 1 can be...

A question: Let bin(a,b) denote the binomial coefficient a! / ( b! (a - b)! ). Is it true that bin( 2p, p ) = 2 (mod p) if p is prime and p>=3 ?

While I know the time complexity for all known prime factorization algorithms is exponential, I can't seem to get this results for a very simple algorithm. First assume we're doing this with numbers that are simply the product of two primes (the kind you get when working with RSA and others)...

Hey all, I have a problem regarding polynomial congruences. I need to find an iterative procedure for solving a polynomial congruence modulo a prime power. I've been working on the case p^2 and I want to ask my question regarding just this case. Hopefully once I understand the proof here I...

If we define a function a(n) with the next properties, a(n) is 1 iff n is prime and 0 if n is composite..then we can write the function a(n) a(n)=\pi(n+1)-\pi(n) where pi(x) is the usual prime number counting function, then my question is to define a b(n) function so b(n)=1 if p and p+2...

I got stuck on one part of this proof. I'm trying to show that (2(p1)(p2)...(pn))^4 + 1 is divisible by an odd prime q. Can anyone help with some suggestions?

Hi, I just wondered what patterns are known about the prime numbers ? cheers roger

I'm trying to create a sieve (prime sieve). A nice quick simple one using boolean expressions. I remember on Visual Basics it began by creating like X number of boolean variables and then sieve them out by classifying them as false... and so on. How to a create a large group of boolean...

When I write out the decimal expansion of 1/p where p is a prime, it is always a recurring decimal with a period per(p). I was thinking why inverting a prime number should always give a recurring decimal but could not think of a reason other than it has to be something to do with our base 10...

Anyone read this? What do you think? http://www.seedmagazine.com/news/2006/03/prime_numbers_get_hitched.php?utm_source=seedmag-main=rss

Problem: "Suppose that G is a group with more than one element and G has no proper, nontrivial subgroups. Prove that |G| is prime. (Do not assume at the outset that G is finite)." Basically, I'm pretty sure I can do this problem. I'm just unsure of how to prove that all infinite groups...

Do you know of an attempt to disprove the existence of a formula which predicts all prime numbers, as opposed to the accustomed attempt to derive one?

Everytime i get a new desk, it's because my old one didn't have enough space. After a while, the new desk ends up not having enough spaces and i go even bigger. Soon i'll have a desk 30 feet long and will still find a way to use up all that space. Sheesh! Oh and even though it deserves its own...

Another new skin, thanks Greg!

Hi, The GIMPS project has found a new Mersenne prime: M43 ! \large 2^{30,402,457} - 1 It is the 43th known Mersenne prime and it is the new largest known prime. It has 9,152,052 digits ! So the BIG ONE (more than 10 millions digits) is still to be found ! (and its discoverer will...

FLT-Solution for prime values of "n". The proof is posted in my journal. It has been blessed by two Math academics. Take a look. By the way, Victor was very close.

Hello, I have this problem that I completed. I was hoping somebody could just let me know, based on my answers if the graph I have drawn looks to be correct? I would really appreciate it. Thanks to anyone who replies. :smile:

I was trying to explain to my family last night why 1 is not generally defined as a prime number and I thought of the Zeta Function. There is the standard way to write it, (1)\zeta(s)=\sum_{n=1}^{\infty}n^{-s} but then there is also the Euler product formula...

I have been working on constructing a method to factor composite numbers composed of two odd prime numbers a and b. As a result, I have been experimenting numerically with various patterns to see if I could find some patterns that would reveal information about composites of two prime numbers...

Any help would be appreciated. I need to show that for all integers of the form 3n+2 there is a prime factor of the same form. I know that integers of this form can be either even or odd depending on what class n falls into, so I thought a logical starting point would be to plug in 2n and...

how to calculate the number of prime factors of 360? please give the method

Just a couple questions that I'd appreciate any help on. 1. if [(2^d) - 1] is prime, prove that d is prime as well. 2. Prove that (p-1)C(k) is congruent to (-1)^k mod p. I've started them both but ended up getting stuck. Any ideas? Thanks

I'm trying to prove that any prime number bigger than 3 is congruent to 1 or 5 modulo 6. I started out by saying that that is the same as saying all prime numbers bigger than 3 are in the form 6n +- 1, n is an integer since 1 or 5 mod 6 yields either 1 or -1 and if you divide 6n+-1 by 6, you...

here's one more: pairs of primes separated by a single number are called prime pairs. Example: 17 and 19 are a pair. Prove that the number between prime pair is always divisible by 6 (assuming both numbers are greater than 6).

You know we always talk about American presidents. I think our friendly neighbour to the north deserves some attention. So I've compiled a list of the most significant prime ministers, let's have a debate!

Prime counting function-- no error. I have developed a prime counting function with no error; it returns the exact number of primes equal to or less than any number one chooses. I am rather ignorant of progress in this field... Has this been done before? Please, ignore any skepticism you...

Hi, I"m working on my math history class project. I choose a topic to discuss about Theory of Ideal Prime Factors by Ernst Eduard Kummer. (1847). I read the material few times, but I don't get an understand of the basic idea how he can come up this theory. Can someone explain it in a...

Hello. I was reading a journal and an interesting problem came up. I believe the journal was in the American Mathematics Society publications. Well, here's the statement. "For all integers, n greater than or equal to 3, the number of compositions of n into relatively prime parts is a...

i have discovered a formula for \pi(x^{a}) being Pi the prime number counting function in terms of a triple integral...but you wll say..this is already made what is this good for?..in fact if you knew \pi(x^{a}) with a total error O(x^d) by setting a=Ad and making A--->oo (infinite) the total...