parisize = 8000000, primelimit = 500000
realprecision = 38011 significant digits (38000 digits displayed)
Welcome to the CHG primality prover!
------------------------------------
Input file is: 7176_24691.in
Certificate file is: 7176_24691.out
Found values of n, F and G.
Number to be tested has 95202 digits.
Modulus has 25721 digits.
Modulus is 27.017160175493079358% of n.
NOTICE: This program assumes that n has passed
a BLS PRP-test with n, F, and G as given. If
not, then any results will be invalid!
Square test passed for F >> G. Using modified right endpoint.
Search for factors congruent to 1.
Running CHG with h = 12, u = 5. Right endpoint has 18040 digits.
Done! Time elapsed: 4270800ms.
Running CHG with h = 12, u = 5. Right endpoint has 17913 digits.
Done! Time elapsed: 3076560ms.
Running CHG with h = 13, u = 5. Right endpoint has 17761 digits.
Done! Time elapsed: 4273530ms.
Running CHG with h = 12, u = 5. Right endpoint has 17558 digits.
Done! Time elapsed: 10909510ms.
Running CHG with h = 13, u = 5. Right endpoint has 17335 digits.
Done! Time elapsed: 8614760ms.
Running CHG with h = 12, u = 5. Right endpoint has 17051 digits.
Done! Time elapsed: 13067180ms.
Running CHG with h = 12, u = 5. Right endpoint has 16819 digits.
Done! Time elapsed: 25482580ms.
Running CHG with h = 12, u = 5. Right endpoint has 16581 digits.
Done! Time elapsed: 8616260ms.
Running CHG with h = 12, u = 5. Right endpoint has 16318 digits.
Done! Time elapsed: 21450800ms.
Running CHG with h = 12, u = 5. Right endpoint has 16030 digits.
Done! Time elapsed: 6250510ms.
Running CHG with h = 11, u = 4. Right endpoint has 15712 digits.
Done! Time elapsed: 3241120ms.
Running CHG with h = 11, u = 4. Right endpoint has 15534 digits.
Done! Time elapsed: 3472190ms.
Running CHG with h = 11, u = 4. Right endpoint has 15245 digits.
Done! Time elapsed: 6200680ms.
Running CHG with h = 11, u = 4. Right endpoint has 14972 digits.
Done! Time elapsed: 7434670ms.
Running CHG with h = 11, u = 4. Right endpoint has 14632 digits.
Done! Time elapsed: 21452800ms.
Running CHG with h = 11, u = 4. Right endpoint has 14205 digits.
Done! Time elapsed: 27942120ms.
Running CHG with h = 11, u = 4. Right endpoint has 13673 digits.
Done! Time elapsed: 35284890ms.
Running CHG with h = 9, u = 3. Right endpoint has 13007 digits.
Done! Time elapsed: 517880ms.
Running CHG with h = 9, u = 3. Right endpoint has 12746 digits.
Done! Time elapsed: 933790ms.
Running CHG with h = 9, u = 3. Right endpoint has 12376 digits.
Done! Time elapsed: 1206830ms.
Running CHG with h = 9, u = 3. Right endpoint has 11936 digits.
Done! Time elapsed: 1244820ms.
Running CHG with h = 9, u = 3. Right endpoint has 11290 digits.
Done! Time elapsed: 1372640ms.
Running CHG with h = 7, u = 2. Right endpoint has 10471 digits.
Done! Time elapsed: 79250ms.
Running CHG with h = 7, u = 2. Right endpoint has 10173 digits.
Done! Time elapsed: 74900ms.
Running CHG with h = 7, u = 2. Right endpoint has 9686 digits.
Done! Time elapsed: 92740ms.
Running CHG with h = 7, u = 2. Right endpoint has 9063 digits.
Done! Time elapsed: 264920ms.
Running CHG with h = 7, u = 2. Right endpoint has 7606 digits.
Done! Time elapsed: 447600ms.
Running CHG with h = 5, u = 1. Right endpoint has 5860 digits.
Done! Time elapsed: 29150ms.
Running CHG with h = 5, u = 1. Right endpoint has 2491 digits.
Done! Time elapsed: 79630ms.
A certificate has been saved to the file: 7176_24691.out
Running David Broadhurst's verifier on the saved certificate...
Testing a PRP called "7176_24691.in".
Pol[1, 1] with [h, u]=[5, 1] has ratio=4.597595982772995048 E-3506 at X, ratio=3.801828163677429171 E-4218 at Y, witness=2.
Pol[2, 1] with [h, u]=[4, 1] has ratio=0.8076550619027120551 at X, ratio=5.798602554199357743 E-3369 at Y, witness=2.
Pol[3, 1] with [h, u]=[7, 2] has ratio=3.217169801397180630 E-13 at X, ratio=4.402750607303828036 E-3493 at Y, witness=11.
Pol[4, 1] with [h, u]=[7, 2] has ratio=1.0000000000000000000 at X, ratio=2.0842962631052741796 E-2914 at Y, witness=2.
Pol[5, 1] with [h, u]=[7, 2] has ratio=0.9490155606269143670 at X, ratio=1.9099332320044321008 E-1247 at Y, witness=2.
Pol[6, 1] with [h, u]=[7, 2] has ratio=4.900545321013125885 E-488 at X, ratio=2.4015344443303641034 E-975 at Y, witness=2.
Pol[7, 1] with [h, u]=[7, 2] has ratio=2.4015344443303641034 E-975 at X, ratio=9.264723012859239110 E-596 at Y, witness=2.
Pol[8, 1] with [h, u]=[9, 3] has ratio=7.432704068703845780 E-955 at X, ratio=4.709306477033762143 E-2457 at Y, witness=2.
Pol[9, 1] with [h, u]=[9, 3] has ratio=0.03485288983087276693 at X, ratio=1.4912796152199036330 E-1939 at Y, witness=2.
Pol[10, 1] with [h, u]=[9, 3] has ratio=0.4798736611128196743 at X, ratio=8.312213958948559530 E-1320 at Y, witness=3.
Pol[11, 1] with [h, u]=[9, 3] has ratio=1.0000000000000000000 at X, ratio=4.937589721111078568 E-1112 at Y, witness=5.
Pol[12, 1] with [h, u]=[9, 3] has ratio=1.1168055224793939179 E-523 at X, ratio=1.0501017405996336266 E-782 at Y, witness=13.
Pol[13, 1] with [h, u]=[11, 4] has ratio=0.5056377836401818539 at X, ratio=3.0570627788653768758 E-2664 at Y, witness=11.
Pol[14, 1] with [h, u]=[11, 4] has ratio=0.18538850554550597892 at X, ratio=1.5021109555506145503 E-2131 at Y, witness=7.
Pol[15, 1] with [h, u]=[11, 4] has ratio=0.3117737228454022066 at X, ratio=1.984546565661947591 E-1705 at Y, witness=19.
Pol[16, 1] with [h, u]=[11, 4] has ratio=0.2826538580527206811 at X, ratio=1.9021090257026318712 E-1364 at Y, witness=2.
Pol[17, 1] with [h, u]=[11, 4] has ratio=0.028147659024124845166 at X, ratio=9.268546666420088546 E-1092 at Y, witness=31.
Pol[18, 1] with [h, u]=[11, 4] has ratio=0.00003188535853697225243 at X, ratio=8.662826235599488434 E-1158 at Y, witness=3.
Pol[19, 1] with [h, u]=[11, 4] has ratio=1.4178215413457083242 E-535 at X, ratio=9.441995651801124555 E-713 at Y, witness=13.
Pol[20, 1] with [h, u]=[12, 5] has ratio=0.05583901374348878402 at X, ratio=2.052870434304672199 E-1587 at Y, witness=7.
Pol[21, 1] with [h, u]=[12, 5] has ratio=0.06680660130173295265 at X, ratio=3.894486481221340852 E-1443 at Y, witness=3.
Pol[22, 1] with [h, u]=[12, 5] has ratio=0.05558051941472609334 at X, ratio=4.803965426101829123 E-1312 at Y, witness=2.
Pol[23, 1] with [h, u]=[12, 5] has ratio=0.09817415991403734273 at X, ratio=9.187976121653162405 E-1193 at Y, witness=19.
Pol[24, 1] with [h, u]=[12, 5] has ratio=1.0000000000000000000 at X, ratio=4.348184146383216996 E-1159 at Y, witness=2.
Pol[25, 1] with [h, u]=[13, 5] has ratio=0.07649480316987622405 at X, ratio=1.1274710699531456660 E-1421 at Y, witness=41.
Pol[26, 1] with [h, u]=[12, 5] has ratio=9.992553673211072144 E-56 at X, ratio=3.798012464019754052 E-1117 at Y, witness=13.
Pol[27, 1] with [h, u]=[13, 5] has ratio=0.5170735828700391153 at X, ratio=2.5605104201289975006 E-1015 at Y, witness=7.
Pol[28, 1] with [h, u]=[12, 5] has ratio=1.0367767222203293471 E-153 at X, ratio=7.334069858782291885 E-762 at Y, witness=5.
Pol[29, 1] with [h, u]=[12, 5] has ratio=1.1856375901542335636 E-128 at X, ratio=4.807780291249966153 E-635 at Y, witness=3.
Validated in 21 sec.
Congratulations! n is prime!
Goodbye!