realprecision = 21019 significant digits (21000 digits displayed) Welcome to the CHG primality prover! ------------------------------------ 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!