mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Software

Reply
 
Thread Tools
Old 2017-11-08, 12:18   #1
alpertron
 
alpertron's Avatar
 
Aug 2002
Buenos Aires, Argentina

13·107 Posts
Default Possible error in PRP calculation or server display

From the information given in Primenet for M3416453, it shows that the PRP residue of M3416453/39603523177 is equal to the PRP residue of M3416453/39603523177/27070715752699810127.

Is this an error on Prime95 or in Primenet? There is a very low probability that all 64 bits of the residue match.
alpertron is offline   Reply With Quote
Old 2017-11-08, 13:47   #2
GP2
 
GP2's Avatar
 
Sep 2003

5×11×47 Posts
Default

Quote:
Originally Posted by alpertron View Post
Is this an error on Prime95 or in Primenet? There is a very low probability that all 64 bits of the residue match.
This is a property of Type 5 residues. The numerical value of the residue remains unchanged, so older results with fewer factors can act as a double-check for the newer result.
GP2 is offline   Reply With Quote
Old 2017-11-08, 14:15   #3
alpertron
 
alpertron's Avatar
 
Aug 2002
Buenos Aires, Argentina

139110 Posts
Default

Where can I find information on how these type 5 PRP residues are calculated?
alpertron is offline   Reply With Quote
Old 2017-11-08, 15:27   #4
Prime95
P90 years forever!
 
Prime95's Avatar
 
Aug 2002
Yeehaw, FL

22×3×641 Posts
Default

From the C code:

Code:
// There are (at least) 5 PRP residue types for testing N=(k*b^n+c)/d:
#define	PRIMNET_PRP_TYPE_FERMAT		1	// Fermat PRP.  Calculate a^(N-1) mod N.  PRP if result = 1
#define	PRIMNET_PRP_TYPE_SPRP		2	// SPRP variant.  Calculate a^((N-1)/2) mod N.  PRP if result = +/-1
#define	PRIMNET_PRP_TYPE_FERMAT_VAR	3	// Type 1 variant,b=2,d=1. Calculate a^(N-c) mod N.  PRP if result = a^-(c-1)
#define	PRIMNET_PRP_TYPE_SPRP_VAR	4	// Type 2 variant,b=2,d=1. Calculate a^((N-c)/2) mod N.  PRP if result = +/-a^-((c-1)/2)
#define	PRIMNET_PRP_TYPE_COFACTOR	5	// Cofactor variant.  Calculate a^(N*d-1) mod N*d.  PRP if result = a^(d-1) mod N.  (d is product of known factors)
Prime95 is offline   Reply With Quote
Old 2017-11-08, 16:07   #5
alpertron
 
alpertron's Avatar
 
Aug 2002
Buenos Aires, Argentina

13×107 Posts
Default

OK. I understand it now the type 5 PRP. Very clever.
alpertron is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
confusing server error messages ramgeis PrimeNet 2 2013-06-09 23:53
ERROR: Workunit not found on server Ungelovende Prime Sierpinski Project 8 2009-09-14 18:00
Mersenne.org Website calculation error joblack Software 0 2009-02-02 02:36
Account Summary Minor Display error Traveller PrimeNet 1 2008-10-31 19:28
ERROR 7:Server has run out of exponents to assign(factoring) dsouza123 Software 4 2003-01-14 11:10

All times are UTC. The time now is 11:02.


Thu Dec 9 11:02:02 UTC 2021 up 139 days, 5:31, 0 users, load averages: 2.29, 1.51, 1.33

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.