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 2017-11-08, 12:18 #1 alpertron     Aug 2002 Buenos Aires, Argentina 25038 Posts 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.
2017-11-08, 13:47   #2
GP2

Sep 2003

13·199 Posts

Quote:
 Originally Posted by alpertron 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.

 2017-11-08, 14:15 #3 alpertron     Aug 2002 Buenos Aires, Argentina 3×449 Posts Where can I find information on how these type 5 PRP residues are calculated?
 2017-11-08, 15:27 #4 Prime95 P90 years forever!     Aug 2002 Yeehaw, FL 11100111011112 Posts 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)
 2017-11-08, 16:07 #5 alpertron     Aug 2002 Buenos Aires, Argentina 3·449 Posts OK. I understand it now the type 5 PRP. Very clever.

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