PARI's commands - Page 95

3.14159 · 2010-08-28, 21:22

Now, to look for a relatively unsearched prime: Primorial. I'll use 45361.

CRGreathouse · 2010-08-28, 21:22

Quote:

Originally Posted by 3.14159

Well, factorization cannot have any restrictions then, except the number must be at least a c90. Factor restriction lifted.

Sounds good.

Quote:

Originally Posted by 3.14159

Okay: Large composites with prime factors no smaller than 50 digits are more impressive.

I was hoping for a general way to transform a vector of the sizes of the prime factors (and possibly a composite cofactor?) into a score that could be ranked, so if I had 100 such factorizations I could decide what was the best, the second best, and so forth. At the origin of your list you used (or seemed to use) "points = size of largest prime factor", which I didn't like because it made a p55 . p90 sound better than a p88 . p89.

3.14159 · 2010-08-28, 21:26

Quote:

Originally Posted by CRGreathouse

Sounds good.

Excellent.

Quote:

Originally Posted by CRGreathouse

I was hoping for a general way to transform a vector of the sizes of the prime factors (and possibly a composite cofactor?) into a score that could be ranked, so if I had 100 such factorizations I could decide what was the best, the second best, and so forth. At the origin of your list you used (or seemed to use) "points = size of largest prime factor", which I didn't like because it made a p55 . p90 sound better than a p88 . p89.

What makes it better is how hard it was to factor it.

Also: Factorization = Complete factorization, unless it is too large.

CRGreathouse · 2010-08-28, 21:34

Quote:

Originally Posted by 3.14159

What makes it better is how hard it was to factor it.

So, in short, you don't have a method for determining the 'winners' for #17 and #18, since you have no way of deciding which of two factorizations is more difficult.

Not a problem for me, but I imagine that would discourage people from submitting an entry.

3.14159 · 2010-08-28, 21:40

Quote:

Originally Posted by CRGreathouse

So, in short, you don't have a method for determining the 'winners' for #17 and #18, since you have no way of deciding which of two factorizations is more difficult.

Well, it depends on the methods you use to factor the number. It would be damn impressive if you factored a number into p60 * p75 by using trial-division alone.

CRGreathouse · 2010-08-28, 22:23

Quote:

Originally Posted by 3.14159

Well, it depends on the methods you use to factor the number. It would be damn impressive if you factored a number into p60 * p75 by using trial-division alone.

A person could make that claim, of course. Or a person could use a nondeterministic method (pick a factor and test).

But this doesn't solve the problem of choosing a winner. Are you going to have different categories for different methods? (And what counts as a different method?) And within a given method, how do you decide what is better?

3.14159 · 2010-08-28, 22:33

Quote:

Originally Posted by CRGreathouse

A person could make that claim, of course. Or a person could use a nondeterministic method (pick a factor and test).

But, how many times would they need to do so before guessing the correct factor?

Quote:

Originally Posted by CRGreathouse

But this doesn't solve the problem of choosing a winner. Are you going to have different categories for different methods? (And what counts as a different method?) And within a given method, how do you decide what is better?

For individual factoring methods? And, concerning what is most impressive, that should be obvious. Numbers with large factors, relative to their size.

3.14159 · 2010-08-28, 22:59

At the moment, I'm searching for k * 45361# + 1 (≈ 19605-19610 digits).

I should get something by 01:00.

CRGreathouse · 2010-08-29, 00:05

Quote:

Originally Posted by 3.14159

But, how many times would they need to do so before guessing the correct factor?

Just once, if they're lucky enough.

I'm trying to help you determine reasonable methods for judging your lists and you seem determined to shrug it off. Ah well.

Quote:

Originally Posted by 3.14159

For individual factoring methods? And, concerning what is most impressive, that should be obvious. Numbers with large factors, relative to their size.

Not obvious at all, because you have multiple factors. If two factorizations have different numbers of factors, or if they have the same number of factors and (sorting them by size) there are corresponding factors that are smaller for one but also a pair of corresponding factors where the other is larger, how do they compare?

p30 . p90 vs. p35 . p85 vs. p34 . p 89.

If you don't have a way to rank them, you don't have a way to decide winners for your two cofactor 'competitions'.

3.14159 · 2010-08-29, 01:07

Quote:

Originally Posted by CRGreathouse

I'm trying to help you determine reasonable methods for judging your lists and you seem determined to shrug it off. Ah well.

All the items are fine, except for Factorization.

Quote:

Originally Posted by CRGreathouse

If you don't have a way to rank them, you don't have a way to decide winners for your two cofactor 'competitions'.

Size of the smallest factor is what places a number as high or low in the scale.

Ex: A number with a smallest factor of 6874713856829275576652590301803216341934585163 is a higher-ranking number than a number with a smallest factor of 86275185784708979, and a number with a smallest factor of 7062362420427661148487418730654866333839957380354935428654077083643909 is higher-ranking than that which has a smallest factor of 6874713856829275576652590301803216341934585163.

3.14159 · 2010-08-29, 01:20

Updates for Special Cofactor and General Cofactor (I decided to keep them):

The size of the largest prime factor is what determines how impressive it is:

Yes, CRG, even 3 * p10000 will be accepted into either Special or General cofactor. The hard part will be proving that the 10000-digit number is a prime number. ECPP is recommended.

It must also conform to restrictions placed in post 1011, for Special Cofactor.

For General Cofactor (Also shared with Special Cofactor), the number must be at least 1000 digits in length.

And, finally:

Reminder: I, (optionally mods), search for the + 1 primes for items 1-19 and twin primes.

Other members, (optionally mods), look for the - 1 primes for items 1-19 and twin primes.

Next notice:

For Special and General Cofactor:

For + 1 searchers, which are me alone, and optionally, the mods:

The cofactor, for Special cofactor must be a + 1 number!

Same goes for - 1 searchers: All other members, mods optional:

Cofactor must be a -1 number!

2010-08-28, 21:22	#1035
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	Now, to look for a relatively unsearched prime: Primorial. I'll use 45361. Last fiddled with by 3.14159 on 2010-08-28 at 21:24

2010-08-29, 01:20	#1045
3.14159 May 2010 Prime hunting commission. 1680₁₀ Posts	Updates for Special Cofactor and General Cofactor (I decided to keep them): The size of the largest prime factor is what determines how impressive it is: Yes, CRG, even 3 * p10000 will be accepted into either Special or General cofactor. The hard part will be proving that the 10000-digit number is a prime number. ECPP is recommended. It must also conform to restrictions placed in post 1011, for Special Cofactor. For General Cofactor (Also shared with Special Cofactor), the number must be at least 1000 digits in length. And, finally: Reminder: I, (optionally mods), search for the + 1 primes for items 1-19 and twin primes. Other members, (optionally mods), look for the - 1 primes for items 1-19 and twin primes. Next notice: For Special and General Cofactor: For + 1 searchers, which are me alone, and optionally, the mods: The cofactor, for Special cofactor must be a + 1 number! Same goes for - 1 searchers: All other members, mods optional: Cofactor must be a -1 number! Last fiddled with by 3.14159 on 2010-08-29 at 01:33

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2010-08-28, 22:59	#1042
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	At the moment, I'm searching for k * 45361# + 1 (≈ 19605-19610 digits). I should get something by 01:00.