realprecision = 28012 significant digits (28000 digits displayed)
Welcome to the CHG primality prover!
------------------------------------
Input file is: 40734_16111.in
Certificate file is: 40734_16111.out
Found values of n, F and G.
Number to be tested has 74267 digits.
Modulus has 20393 digits.
Modulus is 27.458193287113304548% 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 = 10, u = 4. Right endpoint has 13091 digits.
Done! Time elapsed: 592100ms.
Running CHG with h = 10, u = 4. Right endpoint has 12880 digits.
Done! Time elapsed: 673780ms.
Running CHG with h = 10, u = 4. Right endpoint has 12618 digits.
Done! Time elapsed: 659020ms.
Running CHG with h = 10, u = 4. Right endpoint has 12289 digits.
Done! Time elapsed: 771860ms.
Running CHG with h = 10, u = 4. Right endpoint has 11960 digits.
Done! Time elapsed: 1865550ms.
Running CHG with h = 10, u = 4. Right endpoint has 11630 digits.
Done! Time elapsed: 5255770ms.
Running CHG with h = 9, u = 3. Right endpoint has 11258 digits.
Done! Time elapsed: 634360ms.
Running CHG with h = 9, u = 3. Right endpoint has 11102 digits.
Done! Time elapsed: 853630ms.
Running CHG with h = 9, u = 3. Right endpoint has 10914 digits.
Done! Time elapsed: 281610ms.
Running CHG with h = 9, u = 3. Right endpoint has 10663 digits.
Done! Time elapsed: 405790ms.
Running CHG with h = 9, u = 3. Right endpoint has 10329 digits.
Done! Time elapsed: 1651230ms.
Running CHG with h = 9, u = 3. Right endpoint has 9883 digits.
Done! Time elapsed: 1614750ms.
Running CHG with h = 8, u = 3. Right endpoint has 9289 digits.
Done! Time elapsed: 720360ms.
Running CHG with h = 8, u = 3. Right endpoint has 9010 digits.
Done! Time elapsed: 1177930ms.
Running CHG with h = 7, u = 2. Right endpoint has 8686 digits.
Done! Time elapsed: 85540ms.
Running CHG with h = 7, u = 2. Right endpoint has 8535 digits.
Done! Time elapsed: 104910ms.
Running CHG with h = 7, u = 2. Right endpoint has 8324 digits.
Done! Time elapsed: 170890ms.
Running CHG with h = 7, u = 2. Right endpoint has 8008 digits.
Done! Time elapsed: 358530ms.
Running CHG with h = 7, u = 2. Right endpoint has 7534 digits.
Done! Time elapsed: 806910ms.
Running CHG with h = 7, u = 2. Right endpoint has 6823 digits.
Done! Time elapsed: 947480ms.
Running CHG with h = 6, u = 2. Right endpoint has 5608 digits.
Done! Time elapsed: 154440ms.
Running CHG with h = 5, u = 1. Right endpoint has 4971 digits.
Done! Time elapsed: 31840ms.
Running CHG with h = 5, u = 1. Right endpoint has 3047 digits.
Done! Time elapsed: 39830ms.
Running CHG with h = 5, u = 1. Right endpoint has 529 digits.
Done! Time elapsed: 223850ms.
A certificate has been saved to the file: 40734_16111.out
Running David Broadhurst's verifier on the saved certificate...
Testing a PRP called "40734_16111.in".
Pol[1, 1] with [h, u]=[5, 1] has ratio=2.0746195682849381998 E-4482 at X, ratio=1.4484183768135900227 E-5010 at Y, witness=5.
Pol[2, 1] with [h, u]=[4, 1] has ratio=4.591687671079424225 E-1161 at X, ratio=1.2755188475695062339 E-2518 at Y, witness=2.
Pol[3, 1] with [h, u]=[4, 1] has ratio=5.506741126339485269 E-1823 at X, ratio=1.0579520703598122952 E-1924 at Y, witness=13.
Pol[4, 1] with [h, u]=[5, 2] has ratio=2.314516811416860462 E-1911 at X, ratio=1.7497401595520280675 E-1274 at Y, witness=2.
Pol[5, 1] with [h, u]=[7, 2] has ratio=1.0000000000000000000 at X, ratio=1.4319336959782028663 E-2430 at Y, witness=3.
Pol[6, 1] with [h, u]=[7, 2] has ratio=0.5652943240065485511 at X, ratio=8.364105476713622745 E-1423 at Y, witness=13.
Pol[7, 1] with [h, u]=[7, 2] has ratio=0.3353808250481924084 at X, ratio=7.142421923927273892 E-949 at Y, witness=5.
Pol[8, 1] with [h, u]=[7, 2] has ratio=0.4371925050335361950 at X, ratio=9.072674004701774330 E-633 at Y, witness=5.
Pol[9, 1] with [h, u]=[7, 2] has ratio=0.0014807794216913852564 at X, ratio=4.407852517592814796 E-422 at Y, witness=3.
Pol[10, 1] with [h, u]=[6, 2] has ratio=0.9347633297377322032 at X, ratio=1.3785961457417234957 E-303 at Y, witness=2.
Pol[11, 1] with [h, u]=[8, 3] has ratio=0.4201233404700105697 at X, ratio=1.8654613905301410282 E-972 at Y, witness=23.
Pol[12, 1] with [h, u]=[8, 3] has ratio=0.22795242036132283456 at X, ratio=3.3354574628906667948 E-838 at Y, witness=2.
Pol[13, 1] with [h, u]=[9, 3] has ratio=0.11098635948967987873 at X, ratio=4.677490592923544206 E-1783 at Y, witness=19.
Pol[14, 1] with [h, u]=[9, 3] has ratio=0.7787344651397194336 at X, ratio=1.6220872762141191679 E-1337 at Y, witness=5.
Pol[15, 1] with [h, u]=[9, 3] has ratio=0.2591273689466199122 at X, ratio=2.457135208626778580 E-1003 at Y, witness=2.
Pol[16, 1] with [h, u]=[9, 3] has ratio=0.4017637310723480101 at X, ratio=1.0296365623857662819 E-752 at Y, witness=7.
Pol[17, 1] with [h, u]=[9, 3] has ratio=0.22923288146357907292 at X, ratio=9.805773527177072068 E-565 at Y, witness=5.
Pol[18, 1] with [h, u]=[9, 3] has ratio=0.3032833456851888286 at X, ratio=3.421814039303733669 E-468 at Y, witness=19.
Pol[19, 1] with [h, u]=[10, 4] has ratio=0.2872655742473887473 at X, ratio=3.102710796668019221 E-1488 at Y, witness=2.
Pol[20, 1] with [h, u]=[10, 4] has ratio=0.2688928533831372457 at X, ratio=6.627217051203346624 E-1323 at Y, witness=5.
Pol[21, 1] with [h, u]=[10, 4] has ratio=0.07067740238314248717 at X, ratio=1.1143207571236829754 E-1316 at Y, witness=3.
Pol[22, 1] with [h, u]=[10, 4] has ratio=3.502582289983299087 E-19 at X, ratio=1.1323071900759473903 E-1314 at Y, witness=17.
Pol[23, 1] with [h, u]=[10, 4] has ratio=9.724979830186461757 E-264 at X, ratio=7.217920593318674778 E-1052 at Y, witness=7.
Pol[24, 1] with [h, u]=[10, 4] has ratio=9.772157898137144142 E-212 at X, ratio=1.1345480125835036934 E-841 at Y, witness=5.
Validated in 8 sec.
Congratulations! n is prime!
Goodbye!