mersenneforum.org  

Go Back   mersenneforum.org > New To GIMPS? Start Here! > Information & Answers

Reply
 
Thread Tools
Old 2020-12-04, 11:29   #1
ZFR
 
ZFR's Avatar
 
Feb 2008
Bray, Ireland

2×3×19 Posts
Default Why are small exponents worked on again?

Sorry if I missed the reason for this, but I'm getting a few CERT jobs for really small exponents in the 10M range

e.g.
https://www.mersenne.org/report_expo...9448001&full=1

This was factored in 2004. Why was a PRP run on it, then another PRP to DC, then a CERT?

Is this just testing to make sure the CERT system works properly?
ZFR is offline   Reply With Quote
Old 2020-12-04, 12:09   #2
S485122
 
S485122's Avatar
 
Sep 2006
Brussels, Belgium

110011011112 Posts
Default

I think it concerns the cofactor primality testing.
There are options to prevent participating in that kind of work which lies outside the primary GIMPS objectives.

Jacob
S485122 is offline   Reply With Quote
Old 2020-12-04, 12:40   #3
ZFR
 
ZFR's Avatar
 
Feb 2008
Bray, Ireland

2·3·19 Posts
Default

I don't mind participating (and it's not like these take any significant time). Just curious about it.
ZFR is offline   Reply With Quote
Old 2020-12-04, 14:40   #4
PhilF
 
PhilF's Avatar
 
Feb 2005
Colorado

3×193 Posts
Default

Quote:
Originally Posted by ZFR View Post
Sorry if I missed the reason for this, but I'm getting a few CERT jobs for really small exponents in the 10M range

e.g.
https://www.mersenne.org/report_expo...9448001&full=1

This was factored in 2004. Why was a PRP run on it, then another PRP to DC, then a CERT?

Is this just testing to make sure the CERT system works properly?
Actually, a PRP test was not run on this exponent. The PRP test was run on the co-factor (PRP-CF). Then you did the CERT of the PRP-CF test.
PhilF is offline   Reply With Quote
Old 2020-12-04, 15:26   #5
ZFR
 
ZFR's Avatar
 
Feb 2008
Bray, Ireland

11100102 Posts
Default

Quote:
Originally Posted by PhilF View Post
Actually, a PRP test was not run on this exponent. The PRP test was run on the co-factor (PRP-CF). Then you did the CERT of the PRP-CF test.
Ah, OK I get it now. So the PRP is run on M9448001 / 336016843979820474553? And the goal behind it is just looking for very large primes?

And a followup question: If the PRP is positive, how can that large prime be confirmed?

And another one: why was a CERT needed if the PRP is DCed?
ZFR is offline   Reply With Quote
Old 2020-12-04, 16:28   #6
PhilF
 
PhilF's Avatar
 
Feb 2005
Colorado

3×193 Posts
Default

Quote:
Originally Posted by ZFR View Post
Ah, OK I get it now. So the PRP is run on M9448001 / 336016843979820474553? And the goal behind it is just looking for very large primes?

And a followup question: If the PRP is positive, how can that large prime be confirmed?

And another one: why was a CERT needed if the PRP is DCed?
A) Yes, exactly.

B) If the prime is very large, then it can't be confirmed, for now. But the chances of a positive PRP test being composite is very miniscule.

C) I noticed this after I posted my first reply, and don't have an answer. Maybe someone else can enlighten us. :)
PhilF is offline   Reply With Quote
Old 2020-12-04, 16:32   #7
kriesel
 
kriesel's Avatar
 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

13×373 Posts
Default

Quote:
Originally Posted by ZFR View Post
Ah, OK I get it now. So the PRP is run on M9448001 / 336016843979820474553? And the goal behind it is just looking for very large primes?

And a followup question: If the PRP is positive, how can that large prime be confirmed?

And another one: why was a CERT needed if the PRP is DCed?
  1. Either finding a new very large prime, or determining whether the Mersenne number has multiple more factors not yet found. Some people like to fully factor them.
  2. Mprime/prime95 can DC or verify a PRP. But that's not proof. If the number is "small" enough, under ~50,000 decimal digits as I recall, other provers can be used. Sorry, don't remember the name of the software.
  3. A PRP-CF Cert verifies the correctness of the PRP of the cofactor Mn/f. A PRP DC or PRP cert verifies the correctness of the PRP of the Mersenne number Mn. It might also be that someone ran an additional run to test the newer software.

Last fiddled with by kriesel on 2020-12-04 at 16:34
kriesel is online now   Reply With Quote
Old 2020-12-04, 17:28   #8
ZFR
 
ZFR's Avatar
 
Feb 2008
Bray, Ireland

2·3·19 Posts
Default

OK, thanks.
ZFR is offline   Reply With Quote
Old 2020-12-04, 19:57   #9
Prime95
P90 years forever!
 
Prime95's Avatar
 
Aug 2002
Yeehaw, FL

5×7×11×19 Posts
Default

Quote:
Originally Posted by ZFR View Post
And another one: why was a CERT needed if the PRP is DCed?
Not really needed, but....

A cert is cheap and cannot be be gamed.
Matching 64-bit residues could be faked -- though highly unlikely anyone would bother.
Prime95 is offline   Reply With Quote
Old 2020-12-04, 22:50   #10
ZFR
 
ZFR's Avatar
 
Feb 2008
Bray, Ireland

1628 Posts
Default

Quote:
Originally Posted by Prime95 View Post
Not really needed, but....

A cert is cheap and cannot be be gamed.
Matching 64-bit residues could be faked -- though highly unlikely anyone would bother.
OK. Thanks for explaining.
ZFR is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
TF small exponents on GPU? mnd9 GPU Computing 12 2019-10-13 06:11
Bug in generating ECM work for small exponents monsted PrimeNet 6 2019-09-28 03:25
How to tell what's being worked on? Rodrigo LMH > 100M 50 2010-08-23 22:03
P-1 on small exponents markr PrimeNet 18 2009-08-23 17:23
256KB L2 limited to small exponents, but 8MB L3 xorbe Information & Answers 2 2009-02-08 05:08

All times are UTC. The time now is 07:17.

Mon Jan 25 07:17:48 UTC 2021 up 53 days, 3:29, 0 users, load averages: 2.52, 2.69, 2.68

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.