Recent content by abertram28

This is a particularly fun problem! Its on a homework that I already turned in. I used the proof by contradiction method. I just need a clarification point. I started by assuming finite number of primes of form 12k-1. suppose N = (6*P1*P2...*Pn)^2 - 3 and set the congruence...

draw a picture of a geiger counter in a pressurized container. explain that you will use a computer to capture the gieger hits over a broad range of time with background corrections for each time range. you will vary the distance by fixed distance levels and use a fixed source of radiation...

Its interesting that someone mentioned this being high school work. Surprise, IT IS a high school competion. It is hosted and run by GATech, but its this question 4 from version A of the Varsity paper, or question 8 from the version B, and indeed, the answer sheet for both gives 5/11 as the...

this problem is annoying. I've found that the primitive roots of 9 are 2 and 5. since 2|18 it can't be a root. i know via some theorems in my book that if 5 is a primitive root of 3, then its a primitive root of 3^k, and also of 2*3^k. sorry about not using latex, shouldn't need it for...

i wasnt trying to exclude ones that arent fast enough. i really don't care about the issue personally, but judging by the few of you who are posting, you must have some personal stake in this. why the attitude? did i step on someones toes in my first post? you could just kindly correct my...

let me refine the light of the context of my statement. obviously there are trivial solutions. its meaningless as a generator to use the algorithm "2" to generate primes. the context was the generation of primes. if an algorithm tests for primality, reguardless of its method, it isn't...

exactly my point. if one has an efficient way to test for primality. that means that the algorithm isn't generating primes, but possible primes. simple as that. an equally useful algorithm is to take a=1, n=a-1, if a/n is an integer, a is not prime, else n=n-1 until n=2, if no n divides a, a...

hey, I am not ignoring the fact that these procedures produce primes. the fact that you think they are large and that the process is easy is opinion, nothing more. if some of these methods are capable of finding all the primes up to some "large prime" so easily, why do they have to include...

ah, i see. none of these are basic algebraic algorithms. none of them are algebraic and use even a restricted input set! the iterative ones arent really even producing the prime, they are producing forms and testing for primality, its really a multifunction program rather than a single...

there are algorithms that plug in single integers and ALWAYS produce primes? could you provide an example? I am having trouble seeing that one being possible. i mean, i believe that one might be possible using a table of primes as input, but that isn't really an algorthim, unless the algorithm...

ok, i see. I am needing to break (-5/p) into (5/p)(p/5)(-1/p) and solve for all the common congruences? i get (-5/p) = {1 for p congruent to 1,9 (mod 20) and -1 for p congruent to -1,-9 (mod 20)} is that right? *EDIT* oops, don't i need to hit 3,7,13,17? *works on second half*...

I know that any number p-prime, p^k (mod 10) = [p^(k mod 4)] (mod 10) and I also know p^k (mod 100) = [p^(k mod 20)] (mod 100) this means that the number 37^2005 has the same final two digits as 37^5, which is what I used as my answer for the problem. Through some playing around, I found...

Right now binary factorization is making some huge progress, so id stop short of saying there were ANY practical limits to factorizations. especially with how commonly computers make huge advances in processing power and memory size. right now, there are no algorithmic methods of...

I am working on some homework that I already handed in, but I can't get one of the problems. The fourth problem on the HW was to prove the forms of (-1/p), (2/p), (3/p), (-5/p), and (7/p). I did this for -1 and 2 using the quadratic residues and generalizing a form for them. for 3 and 7 i...

M42 isn't prime. this number is the 42nd mersenne prime found, but its NOT M42. its M25964951, that's a notation error. nowhere in the original press release or at www.mersenne.org does it call the 42nd discovered mersenne prime M42, it might not even be the 42nd mersenne prime in order of...