Primality Proof of phi(11491,38284)

OpenPFGW

Primality testing (38284^11491-1)/38283 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 29
Calling Brillhart-Lehmer-Selfridge with factored part 27.15%
(38284^11491-1)/38283 is PRP! (353.6782s+0.0004s)

CHG

   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!

Helper File

Phi(11490,38284)/(106238573731*139897540591*17964554195439674794086479311)
540492148620038900206104039350771
9195676072925529680375724754621
17964554195439674794086479311
1017421713089336185875127861
518475885166291772869
121007491825117741861
195293545165362871
38134219064322001
43875105809023
13903172115373
3760987379371
139897540591
106238573731
2407676171
1286555983
21796531
4488761
4352171
2937127
501841
448111
42187
11491
4597
563
499
313
41
37
31
19
17
13
11
5
5
3
2
2

Prime Factor Certification