realprecision = 21019 significant digits (21000 digits displayed) Welcome to the CHG primality prover! ------------------------------------ Input file is: 38284_11491.in Certificate file is: 38284_11491.out Found values of n, F and G. Number to be tested has 52659 digits. Modulus has 14300 digits. Modulus is 27.154934258855329500% 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 9761 digits. Done! Time elapsed: 4993790ms. Running CHG with h = 12, u = 5. Right endpoint has 9588 digits. Done! Time elapsed: 6153520ms. Running CHG with h = 12, u = 5. Right endpoint has 9390 digits. Done! Time elapsed: 1648190ms. Running CHG with h = 12, u = 5. Right endpoint has 9193 digits. Done! Time elapsed: 8565810ms. Running CHG with h = 11, u = 4. Right endpoint has 8977 digits. Done! Time elapsed: 908110ms. Running CHG with h = 11, u = 4. Right endpoint has 8888 digits. Done! Time elapsed: 1238480ms. Running CHG with h = 11, u = 4. Right endpoint has 8779 digits. Done! Time elapsed: 1112460ms. Running CHG with h = 11, u = 4. Right endpoint has 8642 digits. Done! Time elapsed: 1668020ms. Running CHG with h = 11, u = 4. Right endpoint has 8470 digits. Done! Time elapsed: 1778750ms. Running CHG with h = 11, u = 4. Right endpoint has 8254 digits. Done! Time elapsed: 2472430ms. Running CHG with h = 11, u = 4. Right endpoint has 7986 digits. Done! Time elapsed: 11755210ms. Running CHG with h = 9, u = 3. Right endpoint has 7651 digits. Done! Time elapsed: 370060ms. Running CHG with h = 9, u = 3. Right endpoint has 7604 digits. Done! Time elapsed: 380820ms. Running CHG with h = 9, u = 3. Right endpoint has 7542 digits. Done! Time elapsed: 437420ms. Running CHG with h = 9, u = 3. Right endpoint has 7458 digits. Done! Time elapsed: 398330ms. Running CHG with h = 9, u = 3. Right endpoint has 7346 digits. Done! Time elapsed: 669040ms. Running CHG with h = 9, u = 3. Right endpoint has 7198 digits. Done! Time elapsed: 727690ms. Running CHG with h = 9, u = 3. Right endpoint has 6999 digits. Done! Time elapsed: 643000ms. Running CHG with h = 9, u = 3. Right endpoint has 6735 digits. Done! Time elapsed: 500660ms. Running CHG with h = 9, u = 3. Right endpoint has 6383 digits. Done! Time elapsed: 1803180ms. Running CHG with h = 7, u = 2. Right endpoint has 5913 digits. Done! Time elapsed: 57590ms. Running CHG with h = 7, u = 2. Right endpoint has 5812 digits. Done! Time elapsed: 68090ms. Running CHG with h = 7, u = 2. Right endpoint has 5686 digits. Done! Time elapsed: 83620ms. Running CHG with h = 7, u = 2. Right endpoint has 5490 digits. Done! Time elapsed: 53360ms. Running CHG with h = 7, u = 2. Right endpoint has 5219 digits. Done! Time elapsed: 66860ms. Running CHG with h = 7, u = 2. Right endpoint has 4767 digits. Done! Time elapsed: 62870ms. Running CHG with h = 7, u = 2. Right endpoint has 4135 digits. Done! Time elapsed: 62690ms. Running CHG with h = 5, u = 1. Right endpoint has 3135 digits. Done! Time elapsed: 9960ms. Running CHG with h = 5, u = 1. Right endpoint has 1242 digits. Done! Time elapsed: 87050ms. A certificate has been saved to the file: 38284_11491.out Running David Broadhurst's verifier on the saved certificate... Testing a PRP called "38284_11491.in". Pol[1, 1] with [h, u]=[5, 1] has ratio=8.697966917221075027 E-2016 at X, ratio=8.110613898477651179 E-2527 at Y, witness=5. Pol[2, 1] with [h, u]=[4, 1] has ratio=0.7592458704957498475 at X, ratio=5.317400299045671926 E-1894 at Y, witness=2. Pol[3, 1] with [h, u]=[7, 2] has ratio=0.000000003029415866921646325 at X, ratio=2.868006713495475546 E-2001 at Y, witness=17. Pol[4, 1] with [h, u]=[7, 2] has ratio=0.5439897305820939974 at X, ratio=1.8228905418951341981 E-1264 at Y, witness=2. Pol[5, 1] with [h, u]=[7, 2] has ratio=5.869147301511540233 E-1260 at X, ratio=2.367015416461338394 E-904 at Y, witness=2. Pol[6, 1] with [h, u]=[7, 2] has ratio=0.4165681310039839940 at X, ratio=4.958013474156554003 E-542 at Y, witness=3. Pol[7, 1] with [h, u]=[7, 2] has ratio=2.486117911258129591 E-469 at X, ratio=1.5260751548006579613 E-392 at Y, witness=2. Pol[8, 1] with [h, u]=[7, 2] has ratio=0.19270021400200288764 at X, ratio=4.273323962028882943 E-253 at Y, witness=11. Pol[9, 1] with [h, u]=[7, 2] has ratio=9.794059526366695495 E-105 at X, ratio=3.228627423389737103 E-202 at Y, witness=3. Pol[10, 1] with [h, u]=[9, 3] has ratio=0.5536141089501012039 at X, ratio=9.099249317185099382 E-1411 at Y, witness=3. Pol[11, 1] with [h, u]=[9, 3] has ratio=0.2593102853114880389 at X, ratio=3.648752226312564841 E-1058 at Y, witness=13. Pol[12, 1] with [h, u]=[9, 3] has ratio=0.5023052854575697887 at X, ratio=7.172820229588079348 E-794 at Y, witness=2. Pol[13, 1] with [h, u]=[9, 3] has ratio=0.4578614332505181894 at X, ratio=1.5213835119943941543 E-595 at Y, witness=13. Pol[14, 1] with [h, u]=[9, 3] has ratio=0.16341074272473916052 at X, ratio=7.221026741441227824 E-447 at Y, witness=3. Pol[15, 1] with [h, u]=[9, 3] has ratio=0.09762262083381859660 at X, ratio=2.6662876082464590500 E-335 at Y, witness=2. Pol[16, 1] with [h, u]=[9, 3] has ratio=0.6266206950909276086 at X, ratio=8.827668471289280680 E-252 at Y, witness=2. Pol[17, 1] with [h, u]=[9, 3] has ratio=0.07403772780223820418 at X, ratio=6.375603720947144723 E-189 at Y, witness=11. Pol[18, 1] with [h, u]=[9, 3] has ratio=0.017112766963856590837 at X, ratio=7.548676485785475796 E-142 at Y, witness=2. Pol[19, 1] with [h, u]=[11, 4] has ratio=0.004845673977137351848 at X, ratio=1.4334403667629615777 E-1340 at Y, witness=2. Pol[20, 1] with [h, u]=[11, 4] has ratio=0.4508706414257771291 at X, ratio=1.4470601348810764761 E-1072 at Y, witness=13. Pol[21, 1] with [h, u]=[11, 4] has ratio=0.6015640613339336045 at X, ratio=5.911797940105068442 E-865 at Y, witness=2. Pol[22, 1] with [h, u]=[11, 4] has ratio=0.20547353250076463578 at X, ratio=2.3087444476375052958 E-685 at Y, witness=2. Pol[23, 1] with [h, u]=[11, 4] has ratio=0.4890469876830627146 at X, ratio=2.3168280666083505140 E-548 at Y, witness=3. Pol[24, 1] with [h, u]=[11, 4] has ratio=0.09749848376308985666 at X, ratio=6.601928098437376529 E-439 at Y, witness=2. Pol[25, 1] with [h, u]=[11, 4] has ratio=0.3962323120468104112 at X, ratio=7.076486757458774880 E-357 at Y, witness=17. Pol[26, 1] with [h, u]=[12, 5] has ratio=0.2846358047511717875 at X, ratio=5.846018519800043485 E-1078 at Y, witness=31. Pol[27, 1] with [h, u]=[12, 5] has ratio=0.015737899361183555666 at X, ratio=5.355863038596622243 E-990 at Y, witness=59. Pol[28, 1] with [h, u]=[12, 5] has ratio=0.13941681578787579339 at X, ratio=5.679862202458138712 E-990 at Y, witness=3. Pol[29, 1] with [h, u]=[12, 5] has ratio=3.899089666345545090 E-174 at X, ratio=1.1547272481526660033 E-865 at Y, witness=5. Validated in 7 sec. Congratulations! n is prime! Goodbye!