Sep 2002
Database er0rr
3934_{10} Posts

Quote:
Originally Posted by Batalov
Because there was a ton of them, and even more with >29% (which I didn't submit). The comment there says it all (they are a dataset for anyone who wants to learn CHG in practice).

Testing the one I indicated above:
Factoring N1:
Code:
./pfgw64 o f1000 q"(10^468772*10^125682)/(2*3*6449*138176897)"
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Factoring numbers to 1000% of normal.
(10^468772*10^125682)/(2*3*6449*138176897) has no small factor.
Factoring N+1:
Code:
./pfgw64 o f1000 q"5*10^343081"
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Factoring numbers to 1000% of normal.
5*10^343081 has no small factor.
Helper file chg_helper.6:
Code:
2
3
6449
138176897
2
10^12568
BLS test:
Code:
./pfgw64 tc hchg_helper.6 q"10^468772*10^125681"
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 10^468772*10^125681 [N1/N+1, BrillhartLehmerSelfridge]
Reading factors from helper file chg_helper.6
Running N1 test using base 3
Running N+1 test using discriminant 17, base 1+sqrt(17)
10^468772*10^125681 is Fermat and Lucas PRP! (265.8579s+0.0002s)
File 6.in:
Code:
n=10^468772*10^125681;
F=2*3*6449*138176897;
G=2*10^12568;
CHG.GP script alterations:
Code:
allocatemem(128*1024*1024); \\ Increase stack to 64mb for now
\\ You may have to bump this up to 128M for really
\\ big values of h (say bigger than 12).
(Perhaps a tad too high.)
Code:
worktodofile="TestSuite\/6.in";
certificatefile="TestSuite\/6.out";
Script run:
Code:
gp < CHG.GP
Reading GPRC: /etc/gprc ...Done.
GP/PARI CALCULATOR Version 2.5.1 (released)
amd64 running linux (x8664/GMP5.0.5 kernel) 64bit version
compiled: Jun 4 2012, gcc4.7.0 (Debian 4.7.011)
(readline v6.2 disabled, extended help enabled)
Copyright (C) 20002011 The PARI Group
PARI/GP is free software, covered by the GNU General Public License, and comes
WITHOUT ANY WARRANTY WHATSOEVER.
Type ? for help, \q to quit.
Type ?12 for how to get moral (and possibly technical) support.
parisize = 8000000, primelimit = 500509
*** Warning: new stack size = 134217728 (128.000 Mbytes).
realprecision = 28012 significant digits (28000 digits displayed)
Welcome to the CHG primality prover!

Input file is: TestSuite/6.in
Certificate file is: TestSuite/6.out
Found values of n, F and G.
Number to be tested has 46877 digits.
Modulus has 12581 digits.
Modulus is 26.837741491697310904% of n.
NOTICE: This program assumes that n has passed
a BLS PRPtest with n, F, and G as given. If
not, then any results will be invalid!
Square test passed for G >> F. Using modified right endpoint.
Search for factors congruent to 1.
Running CHG with h = 14, u = 6. Right endpoint has 9148 digits.
Done! Time elapsed: 33937816ms.
Running CHG with h = 14, u = 6. Right endpoint has 8964 digits.
Done! Time elapsed: 30500403ms.
Running CHG with h = 14, u = 6. Right endpoint has 8599 digits.
Done! Time elapsed: 30873974ms.
Running CHG with h = 13, u = 5. Right endpoint has 8104 digits.
Done! Time elapsed: 18542919ms.
Running CHG with h = 13, u = 5. Right endpoint has 7636 digits.
Done! Time elapsed: 18322641ms.
Running CHG with h = 11, u = 4. Right endpoint has 6893 digits.
Done! Time elapsed: 6854132ms.
Running CHG with h = 9, u = 3. Right endpoint has 6300 digits.
Done! Time elapsed: 2077398ms.
Running CHG with h = 9, u = 3. Right endpoint has 5366 digits.
Done! Time elapsed: 2016787ms.
Running CHG with h = 7, u = 2. Right endpoint has 4025 digits.
Done! Time elapsed: 391320ms.
Search for factors congruent to n.
Running CHG with h = 14, u = 6. Right endpoint has 9148 digits.
Done! Time elapsed: 34054669ms.
Running CHG with h = 14, u = 6. Right endpoint has 8964 digits.
Done! Time elapsed: 31192117ms.
Running CHG with h = 14, u = 6. Right endpoint has 8599 digits.
Done! Time elapsed: 31922984ms.
Running CHG with h = 13, u = 5. Right endpoint has 8104 digits.
Done! Time elapsed: 19001912ms.
Running CHG with h = 13, u = 5. Right endpoint has 7636 digits.
Done! Time elapsed: 18952632ms.
Running CHG with h = 11, u = 4. Right endpoint has 6893 digits.
Done! Time elapsed: 7182281ms.
Running CHG with h = 9, u = 3. Right endpoint has 6301 digits.
Done! Time elapsed: 2192084ms.
Running CHG with h = 9, u = 3. Right endpoint has 5366 digits.
Done! Time elapsed: 2159538ms.
Running CHG with h = 7, u = 2. Right endpoint has 4026 digits.
Done! Time elapsed: 422691ms.
A certificate has been saved to the file: TestSuite/6.out
Running David Broadhurst's verifier on the saved certificate...
Testing a PRP called "TestSuite/6.in".
Pol[1, 1] with [h, u]=[7, 2] has ratio=1.4461419357427070131 E6817 at X, ratio=5.664809224989919335 E8988 at Y, witness=3.
Pol[2, 1] with [h, u]=[9, 3] has ratio=7.490470065658087023 E2940 at X, ratio=6.390768475566896671 E4023 at Y, witness=2.
Pol[3, 1] with [h, u]=[7, 3] has ratio=1.2972540577360267584 E1584 at X, ratio=5.256884481953367877 E2804 at Y, witness=6449.
Pol[4, 1] with [h, u]=[9, 4] has ratio=3.145579049895579619 E593 at X, ratio=9.790444610593665637 E2371 at Y, witness=3.
Pol[5, 1] with [h, u]=[10, 5] has ratio=1.0320034758398752235 E2370 at X, ratio=1.2501766403362505471 E3716 at Y, witness=3.
Pol[6, 1] with [h, u]=[12, 5] has ratio=7.216621710650853283 E1552 at X, ratio=2.805395746440191462 E2340 at Y, witness=3.
Pol[7, 1] with [h, u]=[13, 6] has ratio=5.619243606418243319 E496 at X, ratio=3.1482351295087935110 E2972 at Y, witness=6449.
Pol[8, 1] with [h, u]=[13, 6] has ratio=3.1482351295087935110 E2972 at X, ratio=1.5689033180220872231 E2191 at Y, witness=6449.
Pol[9, 1] with [h, u]=[14, 6] has ratio=1.6317340876422533882 E1206 at X, ratio=2.4395522529325717148 E1102 at Y, witness=3.
Pol[1, 2] with [h, u]=[7, 2] has ratio=1.6068243730474522369 E6818 at X, ratio=1.9558887552173445350 E8986 at Y, witness=17.
Pol[2, 2] with [h, u]=[9, 3] has ratio=1.0120641581575526988 E2941 at X, ratio=9.415995163042182551 E4022 at Y, witness=2.
Pol[3, 2] with [h, u]=[7, 3] has ratio=1.3268475765018631634 E1584 at X, ratio=2.0407180404974932762 E2803 at Y, witness=3.
Pol[4, 2] with [h, u]=[9, 4] has ratio=2.430901089616844084 E593 at X, ratio=3.491959138889946426 E2371 at Y, witness=3.
Pol[5, 2] with [h, u]=[10, 5] has ratio=3.680848125044162843 E2371 at X, ratio=2.683030734698952763 E3716 at Y, witness=3.
Pol[6, 2] with [h, u]=[12, 5] has ratio=2.7782166245229885464 E1552 at X, ratio=2.2097959611499136744 E2340 at Y, witness=3.
Pol[7, 2] with [h, u]=[13, 6] has ratio=5.111982063685797886 E496 at X, ratio=1.7845796163124167244 E2972 at Y, witness=3.
Pol[8, 2] with [h, u]=[13, 6] has ratio=1.7845796163124167244 E2972 at X, ratio=7.384962616549326855 E2191 at Y, witness=3.
Pol[9, 2] with [h, u]=[14, 6] has ratio=1.4706302622525914306 E1206 at X, ratio=3.827727300991043488 E1102 at Y, witness=23.
Validated in 6 sec.
Congratulations! n is prime!
Goodbye!
Note: For similarly sized candidates, the closer to a 12.5% factorisation of N^21, the longer a CHG test takes
Last fiddled with by paulunderwood on 20150228 at 11:22
Reason: 25% of N^21 was the wrong thing to say!
