20180329, 14:35  #100 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9985_{10} Posts 
Perhaps, so. I was concerned that there may be some giant_mod bug or a carry count bug similar to one a few years ago.
Anyway, found one ... at a(15) = 220221 (!!) 
20180329, 14:53  #101  
Feb 2017
Nowhere
2^{2}·1,523 Posts 
Quote:
How many candidates for a(15) were sieved out? BTW, it's another "interesting anomaly" that a(4) = a(3)^2 and a(14) = a(13)^2. 

20180329, 16:11  #102 
Jun 2003
3^{4}·67 Posts 
Hmmm... Unfortunately, we can't really rule out s/w issues with regular double check. BTW, does LLR, P95 & PFGW produce comparable residues on these type of numbers?. Perhaps a Gerbicz Error Check implementation for non base2 PRP could be made. It will be much slower (50%?) but atleast could be used to spot check.

20180329, 19:32  #103 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23401_{8} Posts 
Here is my eval of what usually happens in all three tools.
This is a special form. In LLR there is an input ABC template ABC ($a*$b^$c$d)/$e; in P95, PRP=1,b,n,1,"2", and PFGW understands the ABC form as well as recognizes the special form at parse stage. All three tools have adapted over time to do the following on it:
I am tempted to modify the source for this special case e=2, because giant mod is not needed, just compare two values (1 or (b^n+1)/2+1 these should look just fine in limbs of b how they are likely internally stored)  (or multiply by 2 and compare to 2). ...Thus avoiding giants. Another test that I did in limited range: use a1, a2 in pfgw (or similar in other tools); this is not a little bit, but a lot slower, because the special arrangement of exactly 32K blimbs is destroyed. Let's see what happens. I'll tinker with this on the weekends. 
20180331, 02:05  #105 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
5·1,997 Posts 

20180331, 03:03  #106 
Jun 2003
3^{4}×67 Posts 

20180331, 04:35  #107 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23401_{8} Posts 
These are too small to sieve,  PFGW's ~45bit prefactoring looks fine to me.
It would be a different story for m=17, but I am taking a break for now. 
20180331, 13:15  #108 
Feb 2017
Nowhere
2^{2}×1,523 Posts 

20180401, 17:51  #110  
Sep 2002
Database er0rr
10FE_{16} Posts 
Quote:
Code:
time ./pfgw64 k f0 od q"(11559^131072+1)/2"  ../../coding/gwnum/lucasPRP  1 11559 131072 1 Lucas testing on x^2  4*x + 1 ... Is Lucas PRP! real 20m21.514s user 48m14.480s sys 3m17.668s 

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