realprecision = 15008 significant digits (15000 digits displayed)
Welcome to the CHG primality prover!
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Input file is: 34120_11311.in
Certificate file is: 34120_11311.out
Found values of n, F and G.
Number to be tested has 51269 digits.
Modulus has 15179 digits.
Modulus is 29.605163401524163474% 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 = 6, u = 2. Right endpoint has 5735 digits.
Done! Time elapsed: 55090ms.
Running CHG with h = 5, u = 1. Right endpoint has 4622 digits.
Done! Time elapsed: 80840ms.
Running CHG with h = 5, u = 1. Right endpoint has 4185 digits.
Done! Time elapsed: 92250ms.
Running CHG with h = 5, u = 1. Right endpoint has 3310 digits.
Done! Time elapsed: 110290ms.
Running CHG with h = 5, u = 1. Right endpoint has 1559 digits.
Done! Time elapsed: 68540ms.
A certificate has been saved to the file: 34120_11311.out
Running David Broadhurst's verifier on the saved certificate...
Testing a PRP called "34120_11311.in".
Pol[1, 1] with [h, u]=[5, 1] has ratio=4.921144313427970055 E-1807 at X, ratio=6.199740085418355361 E-3366 at Y, witness=3.
Pol[2, 1] with [h, u]=[4, 1] has ratio=4.025428835039836397 E-1751 at X, ratio=7.652071350319689225 E-1751 at Y, witness=3.
Pol[3, 1] with [h, u]=[4, 1] has ratio=7.702229459930194027 E-877 at X, ratio=9.987716197571524824 E-876 at Y, witness=2.
Pol[4, 1] with [h, u]=[4, 1] has ratio=4.729639853553320582 E-439 at X, ratio=1.9305969379067560316 E-438 at Y, witness=2.
Pol[5, 1] with [h, u]=[6, 2] has ratio=7.441555830303143575 E-1114 at X, ratio=5.292272831258085682 E-2226 at Y, witness=3.
Validated in 1 sec.
Congratulations! n is prime!
Goodbye!