GP/PARI CALCULATOR Version 2.13.3 (released)
              amd64 running linux (x86-64/GMP-6.2.1 kernel) 64-bit version
          compiled: Oct 25 2021, gcc version 11.2.0 (Ubuntu 11.2.0-10ubuntu1)
                               threading engine: pthread
                     (readline v8.1 enabled, extended help enabled)

                         Copyright (C) 2000-2020 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 ?17 for how to get moral (and possibly technical) support.

parisize = 8000000, primelimit = 500000, nbthreads = 8
  ***   Warning: new stack size = 536870912 (512.000 Mbytes).
   realprecision = 50014 significant digits (50000 digits displayed)

Welcome to the CHG primality prover!
------------------------------------

Input file is:  92365_24691.in
Certificate file is:  92365_24691.out
Found values of n, F and G.
    Number to be tested has 122599 digits.
    Modulus has 32940 digits.
Modulus is 26.867420021110790498% 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 = 14, u = 6. Right endpoint has 23782 digits.
        Done!  Time elapsed:  9933860ms.
    Running CHG with h = 14, u = 6. Right endpoint has 23384 digits.
        Done!  Time elapsed:  9669012ms.
    Running CHG with h = 14, u = 6. Right endpoint has 22961 digits.
        Done!  Time elapsed:  8906685ms.
    Running CHG with h = 13, u = 5. Right endpoint has 22526 digits.
        Done!  Time elapsed:  4711596ms.
    Running CHG with h = 13, u = 5. Right endpoint has 22312 digits.
        Done!  Time elapsed:  4879146ms.
    Running CHG with h = 13, u = 5. Right endpoint has 21986 digits.
        Done!  Time elapsed:  4620042ms.
    Running CHG with h = 13, u = 5. Right endpoint has 21690 digits.
        Done!  Time elapsed:  4811585ms.
    Running CHG with h = 13, u = 5. Right endpoint has 21304 digits.
        Done!  Time elapsed:  4713306ms.
    Running CHG with h = 13, u = 5. Right endpoint has 20880 digits.
        Done!  Time elapsed:  5129083ms.
    Running CHG with h = 13, u = 5. Right endpoint has 20321 digits.
        Done!  Time elapsed:  6330445ms.
    Running CHG with h = 11, u = 4. Right endpoint has 19545 digits.
        Done!  Time elapsed:  1957517ms.
    Running CHG with h = 11, u = 4. Right endpoint has 19173 digits.
        Done!  Time elapsed:  1912417ms.
    Running CHG with h = 11, u = 4. Right endpoint has 18693 digits.
        Done!  Time elapsed:  1777571ms.
    Running CHG with h = 11, u = 4. Right endpoint has 18162 digits.
        Done!  Time elapsed:  1921192ms.
    Running CHG with h = 11, u = 4. Right endpoint has 17539 digits.
        Done!  Time elapsed:  2069536ms.
    Running CHG with h = 9, u = 3. Right endpoint has 16655 digits.
        Done!  Time elapsed:  516441ms.
    Running CHG with h = 9, u = 3. Right endpoint has 16219 digits.
        Done!  Time elapsed:  583214ms.
    Running CHG with h = 9, u = 3. Right endpoint has 15931 digits.
        Done!  Time elapsed:  608317ms.
    Running CHG with h = 9, u = 3. Right endpoint has 15546 digits.
        Done!  Time elapsed:  515062ms.
    Running CHG with h = 9, u = 3. Right endpoint has 14741 digits.
        Done!  Time elapsed:  563800ms.
    Running CHG with h = 9, u = 3. Right endpoint has 13760 digits.
        Done!  Time elapsed:  531461ms.
    Running CHG with h = 7, u = 2. Right endpoint has 12417 digits.
        Done!  Time elapsed:  109425ms.
    Running CHG with h = 7, u = 2. Right endpoint has 11186 digits.
        Done!  Time elapsed:  128285ms.
    Running CHG with h = 7, u = 2. Right endpoint has 9563 digits.
        Done!  Time elapsed:  111335ms.
    Running CHG with h = 5, u = 1. Right endpoint has 7077 digits.
        Done!  Time elapsed:  11673ms.
    Running CHG with h = 5, u = 1. Right endpoint has 2954 digits.
        Done!  Time elapsed:  9736ms.
A certificate has been saved to the file:  92365_24691.out

Running David Broadhurst's verifier on the saved certificate...

Testing a PRP called "92365_24691.in".

Pol[1, 1] with [h, u]=[5, 1] has ratio=2.6465957398628042790 E-4332 at X, ratio=6.802214999566733530 E-6746 at Y, witness=2.
Pol[2, 1] with [h, u]=[4, 1] has ratio=1.1078032544378937300 E-3237 at X, ratio=5.007041483512086564 E-4123 at Y, witness=2.
Pol[3, 1] with [h, u]=[7, 2] has ratio=1.6582553525473062566 E-8245 at X, ratio=2.491391136783331361 E-4974 at Y, witness=2.
Pol[4, 1] with [h, u]=[7, 2] has ratio=8.371439846877536977 E-1624 at X, ratio=7.008100510988899974 E-3247 at Y, witness=2.
Pol[5, 1] with [h, u]=[7, 2] has ratio=5.250045138392966626 E-2419 at X, ratio=2.4900086218722161226 E-2462 at Y, witness=2.
Pol[6, 1] with [h, u]=[9, 3] has ratio=1.4343076394692276521 E-4029 at X, ratio=1.4343076394692276521 E-4029 at Y, witness=2.
Pol[7, 1] with [h, u]=[9, 3] has ratio=4.002284472103392102 E-1371 at X, ratio=1.6829312818585009175 E-2944 at Y, witness=2.
Pol[8, 1] with [h, u]=[9, 3] has ratio=0.8015436887843473920 at X, ratio=2.0721720076172118000 E-2415 at Y, witness=2.
Pol[9, 1] with [h, u]=[9, 3] has ratio=0.6073594906062747239 at X, ratio=1.2861160173364039898 E-1154 at Y, witness=2.
Pol[10, 1] with [h, u]=[9, 3] has ratio=0.07773694167387068868 at X, ratio=3.711868172410508133 E-866 at Y, witness=17.
Pol[11, 1] with [h, u]=[9, 3] has ratio=8.124493168651349852 E-351 at X, ratio=2.370278033714354033 E-1308 at Y, witness=2.
Pol[12, 1] with [h, u]=[11, 4] has ratio=8.726053724922577115 E-1563 at X, ratio=1.2544068202618376844 E-3533 at Y, witness=2.
Pol[13, 1] with [h, u]=[11, 4] has ratio=4.727090619190449929 E-626 at X, ratio=2.5087502389258144796 E-2496 at Y, witness=17.
Pol[14, 1] with [h, u]=[11, 4] has ratio=0.8383848989493183355 at X, ratio=3.561555659258786197 E-2122 at Y, witness=5.
Pol[15, 1] with [h, u]=[11, 4] has ratio=5.781347762738193315 E-1019 at X, ratio=2.700898703368168856 E-1923 at Y, witness=2.
Pol[16, 1] with [h, u]=[11, 4] has ratio=0.12338652648716530740 at X, ratio=2.6457980489074973737 E-1487 at Y, witness=2.
Pol[17, 1] with [h, u]=[13, 5] has ratio=2.631323782125048675 E-1072 at X, ratio=5.065093821607389414 E-3881 at Y, witness=2.
Pol[18, 1] with [h, u]=[13, 5] has ratio=1.991009881036662560 E-559 at X, ratio=7.066042726336390891 E-2794 at Y, witness=3.
Pol[19, 1] with [h, u]=[13, 5] has ratio=1.1761336189886154868 E-1273 at X, ratio=2.823326515990305194 E-2122 at Y, witness=2.
Pol[20, 1] with [h, u]=[13, 5] has ratio=1.0227905580481556009 E-386 at X, ratio=1.5823416859980017464 E-1929 at Y, witness=11.
Pol[21, 1] with [h, u]=[13, 5] has ratio=0.6013777104567411717 at X, ratio=3.219714014154501060 E-1483 at Y, witness=5.
Pol[22, 1] with [h, u]=[13, 5] has ratio=2.6779252617103771903 E-813 at X, ratio=5.008269833469465246 E-1629 at Y, witness=17.
Pol[23, 1] with [h, u]=[12, 5] has ratio=6.403660102627984046 E-238 at X, ratio=1.4651746356935392232 E-1070 at Y, witness=2.
Pol[24, 1] with [h, u]=[14, 6] has ratio=2.6432755870051564283 E-1163 at X, ratio=7.755291068816337700 E-2609 at Y, witness=2.
Pol[25, 1] with [h, u]=[14, 6] has ratio=2.0671158861869316187 E-163 at X, ratio=2.0262683760754481307 E-2539 at Y, witness=2.
Pol[26, 1] with [h, u]=[14, 6] has ratio=3.614123592378731148 E-399 at X, ratio=1.1137610238961956156 E-2390 at Y, witness=3.

Validated in 19 sec.


Congratulations! n is prime!
Goodbye!