realprecision = 21019 significant digits (21000 digits displayed)
Welcome to the CHG primality prover!
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Input file is: 4529_16381.in
Certificate file is: 4529_16381.out
Found values of n, F and G.
Number to be tested has 59886 digits.
Modulus has 17179 digits.
Modulus is 28.685595588619700532% 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 8351 digits.
Done! Time elapsed: 210890ms.
Running CHG with h = 6, u = 2. Right endpoint has 8207 digits.
Done! Time elapsed: 123230ms.
Running CHG with h = 6, u = 2. Right endpoint has 7992 digits.
Done! Time elapsed: 128740ms.
Running CHG with h = 6, u = 2. Right endpoint has 7670 digits.
Done! Time elapsed: 133820ms.
Running CHG with h = 6, u = 2. Right endpoint has 7186 digits.
Done! Time elapsed: 136130ms.
Running CHG with h = 6, u = 2. Right endpoint has 6460 digits.
Done! Time elapsed: 157590ms.
Running CHG with h = 6, u = 2. Right endpoint has 5530 digits.
Done! Time elapsed: 159940ms.
Running CHG with h = 5, u = 1. Right endpoint has 4599 digits.
Done! Time elapsed: 10370ms.
Running CHG with h = 5, u = 1. Right endpoint has 3472 digits.
Done! Time elapsed: 104630ms.
Running CHG with h = 5, u = 1. Right endpoint has 1218 digits.
Done! Time elapsed: 101610ms.
A certificate has been saved to the file: 4529_16381.out
Running David Broadhurst's verifier on the saved certificate...
Testing a PRP called "4529_16381.in".
Pol[1, 1] with [h, u]=[5, 1] has ratio=5.835561420380681906 E-2768 at X, ratio=7.241302067588751576 E-3985 at Y, witness=23.
Pol[2, 1] with [h, u]=[4, 1] has ratio=4.821602307928439311 E-2066 at X, ratio=3.855075330651802960 E-2255 at Y, witness=2.
Pol[3, 1] with [h, u]=[4, 1] has ratio=2.501770264115215259 E-1128 at X, ratio=4.517070961623805674 E-1128 at Y, witness=2.
Pol[4, 1] with [h, u]=[6, 2] has ratio=0.4680526216804052198 at X, ratio=7.903788472550114062 E-1862 at Y, witness=7.
Pol[5, 1] with [h, u]=[6, 2] has ratio=0.5978687966999096481 at X, ratio=8.297044818334960063 E-1862 at Y, witness=2.
Pol[6, 1] with [h, u]=[6, 2] has ratio=6.266427608611931538 E-727 at X, ratio=2.4854163998922874054 E-1452 at Y, witness=2.
Pol[7, 1] with [h, u]=[6, 2] has ratio=5.971454124140086931 E-485 at X, ratio=4.649925520843198637 E-968 at Y, witness=5.
Pol[8, 1] with [h, u]=[6, 2] has ratio=2.193089460702948020 E-323 at X, ratio=7.474844578358508682 E-646 at Y, witness=23.
Pol[9, 1] with [h, u]=[6, 2] has ratio=8.595018609452281570 E-217 at X, ratio=1.2721507824509890089 E-430 at Y, witness=11.
Pol[10, 1] with [h, u]=[6, 2] has ratio=3.105317986787952453 E-144 at X, ratio=2.5795301518409557634 E-287 at Y, witness=2.
Validated in 1 sec.
Congratulations! n is prime!
Goodbye!