Prime Definition and 756 Threads

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...

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)...

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?

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

[FONT="Century Gothic"]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...

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...