a p83 factor by ECM, the new champion

[R.D. Silverman]

Originally Posted by Mini-Geek

Out of curiosity, how do you do such a thing easily? Edit: actually, on further reflection, it's pretty obvious: from p and sigma, you can calculate the group order, then simply trial factor it to ECM-like bounds and see if it reaches the bounds. You might have to TF hundreds of c83s to find one smooth enough to be realistic, but it seems pretty easy (no significant ECM or QS required on the c83s - if it's hard to factor, it won't work anyway).

Not quite. One would use a combination of TF to some modest bound (say
100K or so), then follow with ECM to find the 7,8, and 9-digit factors
of the group order being tested. TF to 10^9 or 10^10 would be much
too slow.

If one wants an 83-digit composite to be smooth to (say) 10^10
one has u = (83/10), then u^u ~ 4.25 x 10^7. Thus one would need
to search about 42 million random group orders. [By the Canfield-Erdos-Pomerance thm].

[Rich]

In order to avoid any uncertainty, I would be grateful if Bob would state definitively whether his post with picture of the stagily outraged stereotypical German soldier and the animated "Ban" button was intended to convey a real sense of disapproval or not.

[R.D. Silverman]

Originally Posted by Rich

In order to avoid any uncertainty, I would be grateful if Bob would state definitively whether his post with picture of the stagily outraged stereotypical German soldier and the animated "Ban" button was intended to convey a real sense of disapproval or not.

You are joking, right?

You said:

"It is of course possible that the factorization was done by SNFS......... etc"

When you state that a reported record result might have been fudged,
I think it is clear that this is an accusation of possible cheating.

It was totally uncalled for. One does not accuse someone else of even
possible cheating without evidence.

[Mini-Geek]

Originally Posted by R.D. Silverman

Not quite. One would use a combination of TF to some modest bound (say
100K or so), then follow with ECM to find the 7,8, and 9-digit factors
of the group order being tested. TF to 10^9 or 10^10 would be much
too slow.

If one wants an 83-digit composite to be smooth to (say) 10^10
one has u = (83/10), then u^u ~ 4.25 x 10^7. Thus one would need
to search about 42 million random group orders. [By the Canfield-Erdos-Pomerance thm].

If I'm not mistaken, this figure is purely for finding the factor in stage 1. What would it be if you took B2 into account? I'd guess a lower bound would be where u comes from p/B2 instead of p (in this case, 4.6*10^5), since that represents the largest possible prime added due to stage 2.

[R.D. Silverman]

Originally Posted by Mini-Geek

If I'm not mistaken, this figure is purely for finding the factor in stage 1. What would it be if you took B2 into account? I'd guess a lower bound would be where u comes from p/B2 instead of p (in this case, 4.6*10^5), since that represents the largest possible prime added due to stage 2.

To take B2 into account, one would use the Dickman rho-2 function
to estimate the probability that an 83-digit integer has all of its
factors less than a desired B1 plus a single factor between B1 and some
specified B2.

I was just trying to get a quick estimate for how many groups one would
need to look at. The rho-2 estimate would reduce my estimate of 42
million.

[Batalov]

For the sake of the fine art of partial quoting, wasn't the very first post also an accusation?

Originally Posted by R.D. Silverman

Sam just reported that Ryan found a p83 factor of 7,337+ by
ECM !!!!!

This is truly awesome. Unless, of course, it was really done by SNFS.........

Cf (note the partial quoting inside)

Originally Posted by R.D. Silverman

You are joking, right?

You said:

"It is of course possible that the factorization was done by SNFS......... etc"

When you state that a reported record result might have been fudged,
I think it is clear that this is an accusation of possible cheating.

Can we refrain from strawman constructions?
The poster quoted you talking about SNFS, continued your sentence and now suddenly the tables have turned? How interesting.


I am with Paul on this one. The message is easily parsed as a report of a possible shortcut (and we can all agree that the shortcut is valid) and a suggestion for patching the shortcut. Furthermore, compare that suggestion that followed to Brent rules for (his) table of ECM champions - he had some ad hoc safeguards in his tables for a very long time. Brent knew that certain ECM records are constructible (and you undoubtedly know this too); it is just a question of extending the rules. p83 passes the Brent rules.

Just to dot the i's, I don't see an accusation in the message. Maybe I am not a native speaker. Obviously, if there was an accusation in the message, then it would have been equally offending to Sam: the p79 would have been harder to find by ECM than by SNFS (the SNFS difficulty of 11,306+ is ... merely 212!). Now, that is offensive!

[R.D. Silverman]

Originally Posted by Batalov

For the sake of the fine art of partial quoting, wasn't the very first post also an accusation?

Cf (note the partial quoting inside)

Quite clearly it was NOT an accusation of cheating. It was a
suggestion that Sam had not transcribed a reported result correctly
or that the result was reported incorrectly. This was a suggestion that
a purely EDITORIAL error had taken place.

[Batalov]

I know that!
I bet you would have been surprised if that was immediately answered by : ban : or : offensive : smilies by someone.

What happened to "I disapprove of what you say, but I will defend to the death your right to say it" attitude?

[joral]

Originally Posted by Batalov

I know that!
I bet you would have been surprised if that was immediately answered by : ban : or : offensive : smilies by someone.

Would the feelings be slightly different if Bob's speculation came after Ryan posted about it being found with gmp-ecm and posting the log?

[R.D. Silverman]

Originally Posted by Batalov

I know that!
I bet you would have been surprised if that was immediately answered by : ban : or : offensive : smilies by someone.

What happened to "I disapprove of what you say, but I will defend to the death your right to say it" attitude?

An accusation of an editorial error is NOT the same as an accusation of
cheating.

I played professional tournament bridge for a number of years. One thing
one NEVER does is publically accuse an opponent of cheating, even when a highly suspicious result occurs. Instead, one simply writes out a recorder slip
notifying the director of an unusual result. This is not an accusation of
cheating. Unusual results occur. The ACBL keeps records of the recorder
slips and if a pattern of unusual events occurs over time the ACBL looks
into it.

And I have seen some HIGHLY suspicious results. Here is one:

You hold Axx AKQx - 10xxxxx. All Red.

LHO opens 3NT which is alerted as showing a solid minor with no outside
stoppers. Partner jumps to 6S. RHO passes.

Your call? .................

Holding the A trumps, two outside first round controls, and two more
cover cards [KQ hearts], plus ruffs in diamonds, how can one NOT
bid 7S???

The actual player passed. Partner had:

KQJT9x xxxx xx A

Of course hearts don't break, there are no squeezes, so 6S is the limit on the
hand.

Partner has two quick losers in the opponents suit, 3 heart losers and the
trump A missing. A six-loser hand. so WTF is the 6S call??

My partner and I simply filled out a recorder slip.

[Batalov]

Originally Posted by joral

Would the feelings be slightly different if Bob's speculation came after Ryan posted about it being found with gmp-ecm and posting the log?

Well, but they did come after (in an imaginary world of complete knowledge)!
See here (dated Sep.7; open the ECM section)

There is no way of saying something and not be misunderstood by at least someone. Does it make the argument invalid? no! Does it warrant a knee-jerk ...or a suggestion to immediately ? not necessarily!

In a way, there is a similarity in some ECM records to this?

Originally Posted by Backstrom; Oct.2003; SNFS diff=142

GMP-ECM 6.2.3 [powered by GMP 4.3.0] [ECM]
Input number is 17837657355451922652810408444172047764808329085628834562349057700991285509358864423437663868837774542492041869 (110 digits)
Using MODMULN
Using B1=3900000, B2=8561443810, polynomial Dickson(6), sigma=2735675386
dF=16384, k=3, d=158340, d2=11, i0=14
Expected number of curves to find a factor of n digits:
20 25 30 35 40 45 50 55 60 65
3 10 46 260 1790 14489 134864 1418366 1.7e+07 2.2e+08
Step 1 took 8604ms
Using 15 small primes for NTT
Estimated memory usage: 41M
Initializing tables of differences for F took 4ms
Computing roots of F took 264ms
Building F from its roots took 576ms
Computing 1/F took 272ms
Initializing table of differences for G took 4ms
Computing roots of G took 232ms
Building G from its roots took 548ms
Computing roots of G took 220ms
Building G from its roots took 544ms
Computing G * H took 152ms
Reducing G * H mod F took 148ms
Computing roots of G took 220ms
Building G from its roots took 544ms
Computing G * H took 148ms
Reducing G * H mod F took 144ms
Computing polyeval(F,G) took 1016ms
Computing product of all F(g_i) took 8ms
Step 2 took 5144ms
********** Factor found in step 2: 3213162276640339413566047915418064969550383692549981333701
Found probable prime factor of 58 digits: 3213162276640339413566047915418064969550383692549981333701
Probable prime cofactor 5551433702907422298841863964693267244613910158966569 has 52 digits

Does it imply that it is fraudulent? not necessarily.