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1) Message boards : General discussion : Twin Primes and the Polignac Conjecture (Message 30945)
Posted 4645 days ago by Zurtex
Sorry, I was interpreting your proof too much, my point is:

"Any single number p removes a symmetrical repeating pattern of remaining candidates, and can only remove at most 2/p of the remaining candidates in the pattern."

If there are a finite number of twin primes, then you need on remove all the twin primes, that will be sufficient. There can be an infinite number of candidates left, that doesn't matter.
2) Message boards : General discussion : Twin Primes and the Polignac Conjecture (Message 30897)
Posted 4646 days ago by Zurtex
Your approach is a little if off, it starts with the classical proof by contradiction:

Assume "there are a finite number of twin primes"

But you don't make particular use of this and instead attempt to go on and make a counting argument instead, based on prime density and Sieve of Eratosthenes. The counting argument being that only a finite number of twin prime candidates are removed from the infinite set of twin prime candidates using the Sieve of Eratosthenes.

However if we assume here are a finite number of twin primes then it doesn't matter that there are an infinite set of twin prime candidates.
3) Message boards : General discussion : Twin Primes and the Polignac Conjecture (Message 30799)
Posted 4647 days ago by Zurtex
Hi, it's always fun to try your hand at maths but please don't be disappointed with more serious responses if you visit some actual maths boards like: . Mathematicians get a lot of people come to them claiming great proofs when they have lots of mistakes in, and 1 mistake is enough to stop it from being a proof.

Your proof has a lot of erroneous statements in it, try and simplify it to it's actual bare essentials, but I am fairly sure it's false because I think the statement "Any single prime pn can only remove 2/pn of the remaining twin prime pair candidates in the pattern and always removes a symmetrical pattern of pairs." proves your method is insufficient, rather than anything else.

But please feel free to elaborate.
4) Message boards : General discussion : Newbie question. (Message 30017)
Posted 4663 days ago by Zurtex
Factoring a number and to a lesser extent working out if a number is prime or not is one of the most computationally challenging traditional problems.

However, in the last 200 years or so working out if a number is prime or not a "primality test" has got a lot easier thanks to a lot of clever mathematicians. Working out if a "fairly random number" (refereed to as arbitrary) is prime is still quite hard but there's a good method called the AKS test of primality.

However there are even better tests for very specific numbers that match a very specific pattern, these are the ones tested on PrimeGrid. Because the tests are easier it means much much larger numbers can be tested.

The seive tests use a clever algorithm to try and quickly show if a number is composite (not prime), GPUs are fantastic at this algorithm and hence why they are able to show so quickly that so many numbers are composite. In fact I am quite sure that the algorithm, and the programming language below it, will improve at least 10 fold yet. GPUs however are not as good at showing that a number is prime and we will have to rely on CPUs for this.
5) Message boards : General discussion : My First Prime Number (Message 29988)
Posted 4664 days ago by Zurtex
Well done!

And gratz on completing SoB units, I run so much experimental stuff on my computer I crash it too often to get a successful SoB unit completed, so I stick to WU that take less than an hour to crunch these days.
6) Message boards : General discussion : Newbie question. (Message 29279)
Posted 4675 days ago by Zurtex
Indeed you are correct where there are projects designed to find large Mersenne Primes, i.e that of the form M = 2^n -1, they only use known primes for n. As any other numbers are a waste of time and this is provable.

The biggest project to do this was GIMPS, found here:

Where they found 2^43112609 - 1, which is a 12,978,189 digit number. The project now exists mainly just to double check that they haven't missed a smaller Mersenne Prime.

Negative, Fractions, Real and Complex numbers are not considered as sets with prime numbers as you can not use them to derive the nice property like:

"Any integer greater than 1 can be written as a unique product of prime numbers"
7) Message boards : General discussion : Newbie question. (Message 29225)
Posted 4676 days ago by Zurtex
Although an exercise for the reader is to show:

M = (2^n)-1, where M and n are natural numbers, then if M is prime it implies than n is prime.

Which is a nice 1st year undergraduate problem.
8) Message boards : General discussion : Newbie question. (Message 29212)
Posted 4676 days ago by Zurtex
Primes are defined as being greater than 1, this makes it easy to say things like:

"Any integer greater than 1 can be written as a unique product of prime numbers"

If we allowed 1 then we wouldn't have a unique product as we'd always be able to write things like: 5 = 5, 5 = 5*1, 5 = 5*1*1 etc... And 0 is of no use as a prime as x = y * 0 implies x must be 0.

Best app on the web for determining if some arbitrary number is a prime:

Where you'll find 8579697 = 3 x 7 x 19 x 21503

And is therefore not a prime.
9) Message boards : Number crunching : Video Card (Message 9081)
Posted 5615 days ago by Zurtex
And how big of an effect or difference would you say that a video cards GPU would make on such a task as PrimeGrid if it were implemented for this project. Or for the one that it is already working for?

It would potentially be very good for factorization, it would be awful for prime determination.

GPUs are about having lots of small processors that all work very close together to do very fast of the same floating point operations over and over again. So your algorithm needs to be very parallizable and fit the methods in which a GPU runs.

I could imagine that certain types of factorization would fit this really nicely however I've never seen a working algorithm for such a thing, but all the prime determination algorithms I know would be very very poor on a GPU.
10) Message boards : Number crunching : Primegrid running even when it isn\'t? (Message 8362)
Posted 5689 days ago by Zurtex
I have the leave in memory when suspended option on. PrimeGrid is the only project to do this. Even when it says waiting to run, it uses CPU time and the time in the boinc manager increases. I only have two CPU cores. What's up?

I was going to bring this up, I get a lot of funny behaviour like this from PrimeGrid.

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