Wheel factorization: Efficient?

[3.14159]

Originally Posted by CRGreathouse

Given p... that's good. Now we're looking at multiples of a given p > 3 that are 7 mod 24.

Wow. That was rather simple.

Originally Posted by CRGreathouse

OK, more variables. I know what p is: we're given it, and we also know that it's relatively prime with 6 and greater than 1. But what are x and c, and what is the significance of px + c? Is that supposed to equal something else we know?

I'm presuming p means "prime number".

Originally Posted by CRGreathouse

What sequence?

Well, you're going to have to wait until this one is defined. Until then ...

Originally Posted by CRGreathouse

I'm trying to figure out what he means, whether the thing he has in mind is possible or impossible. I'm well able to factor simple expressions, thank you. I'm much less able to interpret what posters here intend. (And not just science_man_88, either, though he's probably one of the hardest.)

How in the hell did you manage to take offense to that? He said your last guess was accurate, and I think he also posted that he wished to find primes using that expression, which I stated was trivially impossible.

[science_man_88]

Originally Posted by CRGreathouse

OK. So my interpretation #3 was somewhat close; what you really meant was
with m,n,p positive integers and p > 1.

Since the right side cannot be divisible by 2 or 3, the factors on the left must be at least 5. Every number > 1 relatively prime to 6 (as the numbers on the left must be) is of the form , so all the equation says is that you have a composite number that is 7 mod 24. Phew! Why didn't you just say so?



Given p... that's good. Now we're looking at multiples of a given p > 3 that are 7 mod 24.



OK, more variables. I know what p is: we're given it, and we also know that it's relatively prime with 6 and greater than 1. But what are x and c, and what is the significance of ? Is that supposed to equal something else we know?



What sequence?



At what point have we eliminated anything?



So far my understanding is that you want to consider numbers that are 7 mod 24 and remove the ones that have a factor (other than the number itself, presumably) of the form . The method of removing these composite 24m + 7 is based on a sequence or sequences unknown.

the sequence given = the OEIS sequence I linked to.

p*x+c p is p, x is a integer, and c is a start value that changes depending on the p chosen. and px+c is a pattern in the m values for 24m+7 that are composite.

[CRGreathouse]

Originally Posted by 3.14159

I saw it as him stating that 6 * n * a prime ± another prime = 24 * n + 7 is always composite. I posted 1567 and 5023.
But now that he clarified and demanded that both p be the same, there will be no primes found there, because an and b in this case share a common divisor, p.

You guessed that he meant p and q when he wrote p and p; I guessed he meant n and m when he wrote n and n. I was the lucky one there, I guess. But if it had been written out properly there would have been no confusion. It's aggravating to me that we're spending so much time trying to understand each other when we share a common language in math that is supposed to be inherently unambiguous.

[CRGreathouse]

Originally Posted by 3.14159

How in the hell did you manage to take offense to that?

I'll admit, I did find your "Just try it for yourself" to be condescending. But I wouldn't say I was offended, as such.

[CRGreathouse]

Originally Posted by 3.14159

I'm presuming p means "prime number".

My interpretation of post #334 is that sm88 does not require p to be prime, only greater than 1.

[3.14159]

Originally Posted by CRGreathouse

You guessed that he meant p and q when he wrote p and p; I guessed he meant n and m when he wrote n and n. I was the lucky one there, I guess.

I guess you were indeed.

Originally Posted by CRGreathouse

But if it had been written out properly there would have been no confusion. It's aggravating to me that we're spending so much time trying to understand each other when we share a common language in math that is supposed to be inherently unambiguous.

Of course there wouldn't. And there still is, because of improper or lack of definition. You need to define a few things first in order for others to understand what you're trying to post, unless it is either already well-defined or self-evident.

The main issue is a lack of definition/consistency.

Originally Posted by CRGreathouse

I'll admit, I did find your "Just try it for yourself" to be condescending. But I wouldn't say I was offended, as such.

Well, apologies. I certainly didn't intend to be condescending.

[science_man_88]

Originally Posted by CRGreathouse

My interpretation of post #334 is that sm88 does not require p to be prime, only greater than 1.

I remembered that as the post went on lol. have you figured what I mean out yet CRGreathouse or anyone else ?

though couldn't you cover that by saying any composite number>2 is a multiple of a prime hence there will be a n such the p = prime will suffice to have all values for the other sequences defined within it?

[CRGreathouse]

Originally Posted by science_man_88

the sequence given = the OEIS sequence I linked to.

I don't remember which you've linked to. The 4^n plus-or-minus-something sequence? The 24n+7 seq? Mersenne primes? Mersenne exponents? Something else?

Originally Posted by science_man_88

p*x+c p is p, x is a integer, and c is a start value that changes depending on the p chosen. and px+c is a pattern in the m values for 24m+7 that are composite.

OK. So we're given a p > 1 and we have a function f. Let f(p) = c. Then you're looking at the values of px + c for all x in some unspecified range. Each one you find (or some of the ones you find) will sieve out composit values of 24m + 7 for m in some unspecified range. Correct?

[3.14159]

Originally Posted by CRGreathouse

My interpretation of post #334 is that sm88 does not require p to be prime, only greater than 1.

Well, if he just requires it to be any positive integer that is not divisible by 2 and 3, why use the variable p at all? p usually means "prime number". Just use "x, where x is coprime to 2 and three"

[CRGreathouse]

Originally Posted by 3.14159

Well, if he just requires it to be any positive integer that is not divisible by 2 and 3, why use the variable p at all? p usually means "prime number". Just use "x, where x is coprime to 2 and three"

Your guess is as good as mine. You can see where I assumed (explicitly!) that it was a prime (before #334), so I was confused as well.

[science_man_88]

Originally Posted by 3.14159

Well, if he just requires it to be any positive integer that is not divisible by 2 and 3, why use the variable p at all? p usually means "prime number". Just use "x, where x is coprime to 2 and three"

p can be just prime as i just said. A002450