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Forum: Math 2012-09-26, 11:20
Replies: 6
Views: 4,539
Posted By Random Poster
That is a false assumption. If an algorithm...

That is a false assumption. If an algorithm relies on a random choice (in this case the iteration function), then it is very likely that any such choice has some pathological inputs for which the...
Forum: Other Mathematical Topics 2012-09-26, 10:49
Replies: 17
Views: 14,394
Posted By Random Poster
But since cosh2(x) - sinh2(x) = 1, cosh(2x) =...

But since cosh2(x) - sinh2(x) = 1, cosh(2x) = 2cosh2(x) - 1, so there should be no need to compute exp(x) to get cosh(x) for any x.
Forum: Factoring 2012-09-16, 08:46
Replies: 74
Views: 7,795
Posted By Random Poster
It doesn't just look like it, it's exactly...

It doesn't just look like it, it's exactly floor(sqrt(2*10^192)).

Has anyone else noticed that there is an entry for "joke" in the index of the book? Can anyone guess (without looking) where it...
Forum: Linux 2012-09-15, 06:48
Replies: 4
Views: 4,306
Posted By Random Poster
The documentation looks like a first draft; each...

The documentation looks like a first draft; each function listed should have its own description page. I expect every one of those will mention quadmath.h once they are written.

gcc may provide...
Forum: Linux 2012-09-14, 06:48
Replies: 4
Views: 4,306
Posted By Random Poster
The examples for the two functions listed under 3...

The examples for the two functions listed under 3 I/O Library Routines (http://gcc.gnu.org/onlinedocs/libquadmath/index.html#toc_I_002fO-Library-Routines) do "#include <quadmath.h>". Of course you...
Forum: Factoring 2012-08-31, 08:11
Replies: 74
Views: 7,795
Posted By Random Poster
Apparently a little less than two weeks was...

Apparently a little less than two weeks was enough. How long will the linear algebra take?
Forum: Factoring 2012-08-19, 08:23
Replies: 74
Views: 7,795
Posted By Random Poster
How is this progressing?

How is this progressing?
Forum: Soap Box 2012-07-29, 09:19
Replies: 711
Views: 57,356
Posted By Random Poster
So what? The last pure gold Olympic medals were...

So what? The last pure gold Olympic medals were awarded exactly one hundred years ago, in the last Olympics before World War One; afterwards they have always been almost pure silver.
Forum: Computer Science & Computational Number Theory 2012-07-25, 06:57
Replies: 103
Views: 14,017
Posted By Random Poster
There seems to be an interesting pattern here: ...

There seems to be an interesting pattern here:

q (mod 16) q^2 (mod 32) bits
0001 or 1111 00001 >=6
0011 or 1101 01001 5
0101 or 1011 11001 >=6...
Forum: FactorDB 2012-07-24, 10:53
Replies: 0
Views: 2,668
Posted By Random Poster
Proven PRPs?

This number (http://factordb.com/index.php?id=1100000000489773674) and this number (http://factordb.com/index.php?id=1100000000518654034) have verified primality certificates (the first one since...
Forum: Puzzles 2012-07-17, 07:17
Replies: 218
Views: 64,968
Posted By Random Poster
By using a not-completely-insane method. In the...

By using a not-completely-insane method. In the outer loop, you take the first N digits of pi; in the inner loop, you take the last M digits of those N digits and test if that number begins with the...
Forum: Soap Box 2012-05-07, 12:57
Replies: 711
Views: 57,356
Posted By Random Poster
It's especially lame when it's based on not...

It's especially lame when it's based on not knowing how the name in question is pronounced. "Qin" is pronounced like "chin", not "kin" as you seem to think.
Forum: YAFU 2012-02-29, 08:06
Replies: 260
Views: 75,532
Posted By Random Poster
It depends on what you mean by "faster". Usually...

It depends on what you mean by "faster". Usually you do ECM for time x which succeeds with probability p, and if it fails you do QS for time y, so the expected total time is x+(1-p)y; this is less...
Forum: YAFU 2012-02-27, 07:45
Replies: 18
Views: 3,859
Posted By Random Poster
Run it under Valgrind on Linux; that can catch...

Run it under Valgrind on Linux; that can catch memory errors even if they wouldn't otherwise lead to a crash.
Forum: Factoring 2012-02-25, 12:51
Replies: 529
Views: 120,735
Posted By Random Poster
That works too, since L(2n)=L(n)^2-2(-1)^n, but...

That works too, since L(2n)=L(n)^2-2(-1)^n, but then you lose the beautiful duality: if you express either F(kn)/F(n) or L(kn)/L(n) as a polynomial in L(n)^2 and the other one as a polynomial in...
Forum: YAFU 2012-02-23, 07:47
Replies: 22
Views: 6,053
Posted By Random Poster
Did you notice that L3105A is the same size as...

Did you notice that L3105A is the same size as L1242 and has a quartic polynomial in F207?
Forum: YAFU 2012-02-21, 08:12
Replies: 22
Views: 6,053
Posted By Random Poster
Or you could do it The Right Way and use...

Or you could do it The Right Way and use x^4+9x^3+26x^2+24x+1 with x=lucas(97)^2.
Forum: Factoring 2012-02-01, 12:56
Replies: 14
Views: 1,693
Posted By Random Poster
Right, monoid is the word I didn't bother to look...

Right, monoid is the word I didn't bother to look up. However, P+-1 can't function solely on multiplication; unless you are extremely lucky, the random element you pick from the monoid is invertible,...
Forum: Factoring 2012-02-01, 12:08
Replies: 14
Views: 1,693
Posted By Random Poster
Only the cyclic subgroup is embedded, not the...

Only the cyclic subgroup is embedded, not the entire elliptic curve. And yes, this is useless for factoring.
Forum: Factoring 2012-01-31, 10:46
Replies: 14
Views: 1,693
Posted By Random Poster
Rings have two distinct associative binary...

Rings have two distinct associative binary operations, but elliptic curves only have one; there is no possible way to define a ring structure on an elliptic curve. P-1 and P+1 certainly do operate on...
Forum: Factoring 2012-01-30, 13:16
Replies: 14
Views: 1,693
Posted By Random Poster
Huh? All three algorithms perform their...

Huh? All three algorithms perform their arithmetic operations in exactly the same ring, the ring of integers modulo the number you want to factor. The difference is the almost-group in which the...
Forum: Programming 2012-01-20, 08:31
Replies: 357
Views: 28,653
Posted By Random Poster
Not quite true; in the context where array is...

Not quite true; in the context where array is defined, sizeof(array) equals 10*sizeof(int) which is likely not the same as sizeof(int*).

There's no difference between these; an expression of the...
Forum: Programming 2012-01-18, 13:17
Replies: 357
Views: 28,653
Posted By Random Poster
Nonsense. typedef char array[]; array...

Nonsense.

typedef char array[];

array foo(array a);
works perfectly well. (Of course, this is no different from "char *foo(char *a)" but still...)
Forum: FactorDB 2012-01-08, 10:21
Replies: 96
Views: 36,474
Posted By Random Poster
Why do you expect the database to recognize a...

Why do you expect the database to recognize a "maxdig" parameter?
Forum: Puzzles 2011-12-31, 10:22
Replies: 25
Views: 2,650
Posted By Random Poster
That is the only possible solution in...

That is the only possible solution in one-dimensional space. In spaces with more dimensions (like the one we happen to live in) there is an infinity of other solutions, because the photons aren't...
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