realprecision = 24005 significant digits (24000 digits displayed)
Welcome to the CHG primality prover!
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Input file is: 9082_15091.in
Certificate file is: 9082_15091.out
Found values of n, F and G.
Number to be tested has 59729 digits.
Modulus has 16199 digits.
Modulus is 27.120603843096306510% 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 = 12, u = 5. Right endpoint has 11133 digits.
Done! Time elapsed: 1232870ms.
Running CHG with h = 12, u = 5. Right endpoint has 10966 digits.
Done! Time elapsed: 1194690ms.
Running CHG with h = 12, u = 5. Right endpoint has 10765 digits.
Done! Time elapsed: 5771100ms.
Running CHG with h = 12, u = 5. Right endpoint has 10562 digits.
Done! Time elapsed: 5731300ms.
Running CHG with h = 12, u = 5. Right endpoint has 10352 digits.
Done! Time elapsed: 10710740ms.
Running CHG with h = 11, u = 4. Right endpoint has 10120 digits.
Done! Time elapsed: 1033720ms.
Running CHG with h = 11, u = 4. Right endpoint has 10026 digits.
Done! Time elapsed: 1395860ms.
Running CHG with h = 11, u = 4. Right endpoint has 9909 digits.
Done! Time elapsed: 1981890ms.
Running CHG with h = 11, u = 4. Right endpoint has 9762 digits.
Done! Time elapsed: 1814880ms.
Running CHG with h = 11, u = 4. Right endpoint has 9575 digits.
Done! Time elapsed: 3683950ms.
Running CHG with h = 11, u = 4. Right endpoint has 9345 digits.
Done! Time elapsed: 3960540ms.
Running CHG with h = 11, u = 4. Right endpoint has 9057 digits.
Done! Time elapsed: 18916260ms.
Running CHG with h = 11, u = 4. Right endpoint has 8697 digits.
Done! Time elapsed: 19970550ms.
Running CHG with h = 9, u = 3. Right endpoint has 8247 digits.
Done! Time elapsed: 564200ms.
Running CHG with h = 9, u = 3. Right endpoint has 8070 digits.
Done! Time elapsed: 405180ms.
Running CHG with h = 9, u = 3. Right endpoint has 7835 digits.
Done! Time elapsed: 287220ms.
Running CHG with h = 9, u = 3. Right endpoint has 7520 digits.
Done! Time elapsed: 306680ms.
Running CHG with h = 9, u = 3. Right endpoint has 7101 digits.
Done! Time elapsed: 2405370ms.
Running CHG with h = 7, u = 2. Right endpoint has 6543 digits.
Done! Time elapsed: 548060ms.
Running CHG with h = 7, u = 2. Right endpoint has 6394 digits.
Done! Time elapsed: 672070ms.
Running CHG with h = 7, u = 2. Right endpoint has 6096 digits.
Done! Time elapsed: 44790ms.
Running CHG with h = 7, u = 2. Right endpoint has 5695 digits.
Done! Time elapsed: 123470ms.
Running CHG with h = 7, u = 2. Right endpoint has 4712 digits.
Done! Time elapsed: 183360ms.
Running CHG with h = 5, u = 1. Right endpoint has 3588 digits.
Done! Time elapsed: 16310ms.
Running CHG with h = 5, u = 1. Right endpoint has 1446 digits.
Done! Time elapsed: 40780ms.
A certificate has been saved to the file: 9082_15091.out
Running David Broadhurst's verifier on the saved certificate...
Testing a PRP called "9082_15091.in".
Pol[1, 1] with [h, u]=[5, 1] has ratio=2.8598921814885988334 E-2261 at X, ratio=2.503359212293993857 E-2811 at Y, witness=3.
Pol[2, 1] with [h, u]=[4, 1] has ratio=0.3985198549268837793 at X, ratio=2.0974201932765759114 E-2142 at Y, witness=23.
Pol[3, 1] with [h, u]=[7, 2] has ratio=9.767215860326297502 E-13 at X, ratio=7.190332131226196698 E-2249 at Y, witness=13.
Pol[4, 1] with [h, u]=[7, 2] has ratio=0.9999999999993286748 at X, ratio=1.4906755391344433729 E-1966 at Y, witness=3.
Pol[5, 1] with [h, u]=[7, 2] has ratio=0.7126291568689247449 at X, ratio=9.915035396793596977 E-803 at Y, witness=17.
Pol[6, 1] with [h, u]=[7, 2] has ratio=3.559804514083092834 E-381 at X, ratio=2.7430927985751780012 E-596 at Y, witness=3.
Pol[7, 1] with [h, u]=[7, 2] has ratio=2.7430927985751780012 E-596 at X, ratio=1.6562284862225918138 E-298 at Y, witness=3.
Pol[8, 1] with [h, u]=[9, 3] has ratio=0.05667185694747806676 at X, ratio=1.0947574748839064900 E-1676 at Y, witness=3.
Pol[9, 1] with [h, u]=[9, 3] has ratio=0.5284676885014765429 at X, ratio=1.3352840603983531846 E-1257 at Y, witness=11.
Pol[10, 1] with [h, u]=[9, 3] has ratio=0.10637803750357910010 at X, ratio=2.1955536605370562588 E-943 at Y, witness=5.
Pol[11, 1] with [h, u]=[9, 3] has ratio=0.12245267478358121479 at X, ratio=8.710662125225153131 E-708 at Y, witness=7.
Pol[12, 1] with [h, u]=[9, 3] has ratio=0.3390976382665094861 at X, ratio=5.184030645982408452 E-531 at Y, witness=2.
Pol[13, 1] with [h, u]=[11, 4] has ratio=0.14585331367970437011 at X, ratio=3.815072355612267404 E-1800 at Y, witness=2.
Pol[14, 1] with [h, u]=[11, 4] has ratio=0.11633046556273361902 at X, ratio=3.130571451766442157 E-1440 at Y, witness=3.
Pol[15, 1] with [h, u]=[11, 4] has ratio=0.4225150802326976844 at X, ratio=2.3912869086164155122 E-1152 at Y, witness=2.
Pol[16, 1] with [h, u]=[11, 4] has ratio=0.3840707375616814661 at X, ratio=4.773902473303361651 E-922 at Y, witness=3.
Pol[17, 1] with [h, u]=[11, 4] has ratio=6.596757259613828200 E-236 at X, ratio=7.911663944916507808 E-747 at Y, witness=5.
Pol[18, 1] with [h, u]=[11, 4] has ratio=0.09405395758322078881 at X, ratio=1.4629793976104511277 E-588 at Y, witness=11.
Pol[19, 1] with [h, u]=[11, 4] has ratio=0.23803150180847264332 at X, ratio=5.593942889984637266 E-471 at Y, witness=11.
Pol[20, 1] with [h, u]=[11, 4] has ratio=0.12373803928998745950 at X, ratio=5.684014534856131042 E-377 at Y, witness=3.
Pol[21, 1] with [h, u]=[12, 5] has ratio=0.5659805900880728071 at X, ratio=1.0783000041433717972 E-1157 at Y, witness=3.
Pol[22, 1] with [h, u]=[12, 5] has ratio=0.03369209106309316607 at X, ratio=1.4704931083397995351 E-1052 at Y, witness=2.
Pol[23, 1] with [h, u]=[12, 5] has ratio=0.011840735803376724403 at X, ratio=1.6666603493253789171 E-1018 at Y, witness=13.
Pol[24, 1] with [h, u]=[12, 5] has ratio=7.644153892406875987 E-165 at X, ratio=1.2473154825156209833 E-1003 at Y, witness=2.
Pol[25, 1] with [h, u]=[12, 5] has ratio=3.339708056926087461 E-168 at X, ratio=1.5632801326973244923 E-836 at Y, witness=5.
Validated in 11 sec.
Congratulations! n is prime!
Goodbye!