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Old 2008-01-15, 20:28   #12
Jean Penné
 
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Default Gathered results for k*2^n+1, n odd

Gary,

I am gathering my results about the four conjectures, which requires a lot of work...
So, we will be able to compare with your results!

Here for +1 and n odd : There are 23 remaining candidates, and 42 primes found.

1) Remaining :

Code:
  k       2k       tested up to (n-1 base 2)

9267    18534         1967862
32247   64494         1770506
37953   75906           33448
38463   76926           34320
39297   78594           35166
50433   100866          46076
53133   106266          87428
56643   113286          33348
60357   120714          46166
60963   121926          32912
61137   122274          33150
62307   124614          35342
70467   140934          46358
75183   150366          32840
78153   156306          32976
78483   156966          33096
78753   157506          55640
80463   160926          35660
84363   168726          35008
85287   170574          33106
91437   182874          33034
93477   186954          34846
93663   187326          67844
2) Primes :

Code:
Normalized	As discovered
 k         n
93       20917	186*2^20916+1 is prime!  Time: 786.013 ms.
2943    108041	5886*2^108040+1 is prime! by Jean Penné 06/02/05, 09:28AM
5193      4277	10386*2^4276+1 is prime!  Time: 59.124 ms.
5703      5149	11406*2^5148+1 is prime!  Time: 99.286 ms.
5823      8105	11646*2^8104+1 is prime!  Time: 384.321 ms.
6807      4415	13614*2^4414+1 is prime!  Time: 64.834 ms.
6843     14753	13686*2^14752+1 is prime!  Time: 935.778 ms.
7233      4277	14466*2^4276+1 is prime!  Time: 58.406 ms.
9777     18975	19554*2^18974+1 is prime!  Time: 791.931 ms.
10923     6801	21846*2^6800+1 is prime!  Time: 177.623 ms.
14397     4347	28794*2^4346+1 is prime!  Time: 59.056 ms.
16917    12799	33834*2^12798+1 is prime!  Time: 829.050 ms.
17457    29563	34914*2^29562+1 is prime! by tcadigan 28/01/05, 07:13AM
17937    53927	35874*2^53926+1 is prime! by tcadigan 28/01/05, 06:41AM
20997     8191	41994*2^8190+1 is prime!  Time: 384.323 ms.
22653    28969	45306*2^28968+1 is prime! by Mark 27/01/05, 11:29PM
24693   357417	49386*2^357416+1 is Prime! by Footmaster 25/05/05, 08:44AM
25083    24981	50166*2^24980+1 is prime! by Mark 27/01/05, 11:29PM
25917     9671	51834*2^9670+1 is prime!  Time: 447.572 ms.
26613    89749	53226*2^89748+1 is prime!  Time: 25.000 sec.
30933     4433	61866*2^4432+1 is prime!  Time: 59.831 ms.
35787    36639	71574*2^36638+1 is prime!  Time: 6.016 sec.
40857     5383	81714*2^5382+1 is prime!  Time: 154.925 ms.
42993    16165	85986*2^16164+1 is prime!  Time: 1.223 sec.
43167     9795	86334*2^9794+1 is prime!  Time: 403.492 ms.
46623    79553	93246*2^79552+1 is prime!  Time: 28.184 sec.
49563     5813	99126*2^5812+1 is prime!  Time: 186.733 ms.
60273     7421	120546*2^7420+1 is prime!  Time: 218.279 ms.
63357     4211	126714*2^4210+1 is prime!  Time: 136.667 ms.
65223     4189	130446*2^4188+1 is prime!  Time: 136.782 ms.
65253    10301	130506*2^10300+1 is prime!  Time: 427.195 ms.
67917    13079	135834*2^13078+1 is prime!  Time: 644.241 ms.
69963     5205	139926*2^5204+1 is prime!  Time: 152.156 ms.
72537    15771	145074*2^15770+1 is prime!  Time: 1.199 sec.
73023    17965	146046*2^17964+1 is prime!  Time: 1.349 sec.
78543    10089	157086*2^10088+1 is prime!  Time: 419.114 ms.
80517     5423	161034*2^5422+1 is prime!  Time: 154.232 ms.
81147    17615	162294*2^17614+1 is prime!  Time: 1.331 sec.
82197     5079	164394*2^5078+1 is prime!  Time: 149.421 ms.
88863     9825	177726*2^9824+1 is prime!  Time: 405.011 ms.
91383    15333	182766*2^15332+1 is prime!  Time: 1.173 sec.
93033    30473	186066*2^30472+1 is prime!  Time: 5.037 sec.
Note : The name of the discoverer is shown only for primes found by the Sierpinski base 4 project.

Regards,
Jean
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Old 2008-01-15, 21:39   #13
gd_barnes
 
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For the Sierp odd-n conjecture, here's an update of both lists with the primes that I found and the Sierp base 4 primes with even k's removed from my list. There was only 1 Sierp base 4 prime not on my list. I ended up testing up to n=118K on all k's before stopping.

I was a little confused as to why you have three k's on your list that have a prime at n=1.

This balancing should make things much easier.

Your list with my primes and test limits:
Code:
                    tested to
  k       2k        (n-1 base 2)     prime
9267    18534         1967862
32247   64494         1770506
37953   75906           118K
38463   76926                        58753
39297   78594           118K
50433   100866          118K
53133   106266          118K
56643   113286                       1     (??) 56643*2^1+1 is prime!
60357   120714          118K
60963   121926                       73409
61137   122274          118K
62307   124614                       44559
70467   140934          118K
75183   150366                       35481
78153   156306                       1     (??) 78153*2^1+1 is prime!
78483   156966                       1     (??) 78483*2^1+1 is prime!
78753   157506                       63761
80463   160926          118K
84363   168726          118K
85287   170574          118K
91437   182874          118K
93477   186954                       63251
93663   187326                       82317

My list with Sierp base 4 primes and test limits and removal of even k's:
Code:
  k     prime     test limit     comments
2943    108041
9267              1.97M          Sierp base 4
17937   53927
24693   357417                   Sierp base 4
26613   89749
32247             1.77M          Sierp base 4
35787   36639
37953             118K
38463   58753
39297             118K
46623   79553
50433             118K
53133             118K
60357             118K
60963   73409
61137             118K
62307   44559
70467             118K
75183   35481
78753   63761
80463             118K
84363             118K
85287             118K
91437             118K
93477   63251
93663   82317

The bottom line as now shown on both lists is that we have 13 k's remaining, 11 of which have been tested to n=118K and the other 2 of which have been tested very high with Sierp base 4. This balances with the 14 odd k's that I said I had remaining previously minus the one removed from Sierp base 4.


Gary

Last fiddled with by gd_barnes on 2008-01-15 at 21:50
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Old 2008-01-16, 08:13   #14
Jean Penné
 
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Quote:
Originally Posted by gd_barnes View Post
For the Sierp odd-n conjecture, here's an update of both lists with the primes that I found and the Sierp base 4 primes with even k's removed from my list. There was only 1 Sierp base 4 prime not on my list. I ended up testing up to n=118K on all k's before stopping.

I was a little confused as to why you have three k's on your list that have a prime at n=1.

This balancing should make things much easier.

Your list with my primes and test limits:
Code:
                    tested to
  k       2k        (n-1 base 2)     prime
9267    18534         1967862
32247   64494         1770506
37953   75906           118K
38463   76926                        58753
39297   78594           118K
50433   100866          118K
53133   106266          118K
56643   113286                       1     (??) 56643*2^1+1 is prime!
60357   120714          118K
60963   121926                       73409
61137   122274          118K
62307   124614                       44559
70467   140934          118K
75183   150366                       35481
78153   156306                       1     (??) 78153*2^1+1 is prime!
78483   156966                       1     (??) 78483*2^1+1 is prime!
78753   157506                       63761
80463   160926          118K
84363   168726          118K
85287   170574          118K
91437   182874          118K
93477   186954                       63251
93663   187326                       82317

My list with Sierp base 4 primes and test limits and removal of even k's:
Code:
  k     prime     test limit     comments
2943    108041
9267              1.97M          Sierp base 4
17937   53927
24693   357417                   Sierp base 4
26613   89749
32247             1.77M          Sierp base 4
35787   36639
37953             118K
38463   58753
39297             118K
46623   79553
50433             118K
53133             118K
60357             118K
60963   73409
61137             118K
62307   44559
70467             118K
75183   35481
78753   63761
80463             118K
84363             118K
85287             118K
91437             118K
93477   63251
93663   82317

The bottom line as now shown on both lists is that we have 13 k's remaining, 11 of which have been tested to n=118K and the other 2 of which have been tested very high with Sierp base 4. This balances with the 14 odd k's that I said I had remaining previously minus the one removed from Sierp base 4.


Gary

Good work, Gary!

I agree for the three k's that must be eliminated because they yield a prime for n = 1 which is, indeed, an odd exponent!!

Here are the gathered results for +1, n even :

1) Remaining :

Code:
  k       tested up to (n base 2)

23451        1950964
60849        1907154
Indeed, all are from Sierpinski base 4 project.

2) Primes :

Code:
2379*2^8114+1 is prime!  Time: 85.883 ms.
8139*2^25954+1 is prime! by Citrix 01/02/05, 06:08AM
9609*2^5422+1 is prime!  Time: 68.815 ms.
10281*2^7444+1 is prime!  Time: 186.376 ms.
11709*2^6882+1 is prime!  Time: 176.373 ms.
12711*2^5092+1 is prime!  Time: 67.712 ms.
14661*2^91368+1 is prime! by Jean Penné 27/01/05, 10:03PM
15441*2^20584+1 is prime! by Footmaster  27/01/05, 03:17PM
17169*2^6450+1 is prime!  Time: 168.967 ms.
21069*2^23006+1 is prime! by Footmaster  27/01/05, 03:51PM
21699*2^72874+1 is prime! by Footmaster 27/01/05, 06:43PM
23799*2^105890+1 is prime! by Ken_g6 29/01/05, 05:45PM
23901*2^11292+1 is prime!  Time: 801.239 ms.
30579*2^48594+1 is prime! by Mark 28/01/05, 12:02AM
33771*2^178200+1 is prime! byJean Penné  29/01/05, 08:10PM
33879*2^378022+1 is prime! by Footmaster 20/06/05, 12:21PM
35889*2^7770+1 is prime!  Time: 372.790 ms.
39231*2^13716+1 is prime!  Time: 924.592 ms.
39759*2^4594+1 is prime!  Time: 61.723 ms.
40269*2^8458+1 is prime!  Time: 389.306 ms.
41289*2^13514+1 is prime!  Time: 917.695 ms.
41709*2^80594+1 is prime! by geoff 29/01/05, 05:38AM
42717*2^905792+1 is prime! by Jean Penné 14/10/05, 08:18PM
44469*2^13134+1 is prime!  Time: 841.834 ms.
51171*2^93736+1 is prime! by masser 31/01/05, 04:18PM
52419*2^4578+1 is prime!  Time: 61.466 ms.
52701*2^6976+1 is prime!  Time: 177.811 ms.
52839*2^32558+1 is prime! by masser 27/01/05, 11:19PM
53979*2^7590+1 is prime!  Time: 367.499 ms.
55611*2^40212+1 is prime! by Citrix 29/01/05, 05:46PM
56019*2^8094+1 is prime!  Time: 379.657 ms.
56139*2^4858+1 is prime!  Time: 64.132 ms.
58791*2^79420+1 is prime! by Mystwalker 27/01/05, 11:21PM
60891*2^40144+1 is prime! by Jean Penné  29/01/05, 09:30AM
61371*2^12576+1 is prime!  Time: 821.165 ms.
62391*2^5472+1 is prime!  Time: 124.840 ms.
63411*2^72064+1 is prime! by Footmaster  31/01/05, 06:05PM
Regards,
Jean
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Old 2008-01-16, 17:44   #15
gd_barnes
 
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Default +1 odd-n conjecture web page update document

Karsten,

Attached is a notepad document that is an update of the web page that you sent me via PM that has many primes filled in and some corrections for the +1 odd-n conjecture. 6 of the k's had primes at n=1; 3 of which already had a higher prime and 3 of which had no prime found.

This balances with the 13 k's remaining at n=118K shown earlier in this thread.


Gary
Attached Files
File Type: txt remain-sierp-base2-oddn.txt (2.1 KB, 246 views)
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Old 2008-01-19, 00:00   #16
gd_barnes
 
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I am also proposing that this thread be moved to the "Conjectures 'R Us" project thread.

As discussed with Jean, we will be adding the Riesel and Seirp base 2 even-n and odd-n conjectures as a subproject to our project.

As with the other threads, I'll wait a couple of days before requesting that this be moved.


Gary
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Old 2008-01-19, 14:44   #17
Jean Penné
 
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Default Just for fun and curiosity...

To illustraste the dissymetry between +1, base 2 odd / even exponents, I tested k = 18534/2 = 9267 with even exponents.
In less than 48H, I found that :

9267*2^n+1 is prime for

n = 100, 1556, 1966, 2660, 4342, 4468, 5372, 39538, 65386, 142426

although for odd exponents, I am presently reaching n = 1983943 with no prime!

I will continue even n during some days, just for fun...

Jean
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Old 2008-01-19, 17:22   #18
Jean Penné
 
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Default Gathered results for -1, base 2 even and odd n's

Here are my gathered rsults for k*2^n-1 even and odd exponents.

(I think all these results would be moved in the new projects as soon as possible...)

Even n's, 4 k's remaining to be tested :

Code:
 k	tested up to (n base 2)

9519	562416
14361	318510
19401	262578
20049	265144
Even n's, 19 primes found / known :

Code:
Normalized	As discovered					Keller freq.
 k         n

2181	 37890	2181*2^37890-1 is prime!  Time : 3.036 sec.	f15
6549	  5076	6549*2^5076-1 is prime!  Time : 35.101 ms.	f12
8181	  8018	8181*2^8018-1 is prime!  Time : 71.021 ms.	f12
8961	 30950	8961*2^30950-1 is prime!  Time : 2.395 sec.	f14
11379	 32252	11379*2^32252-1 is prime!  Time : 2.594 sec.	f14
12849	  9788	12849*2^9788-1 is prime!  Time : 150.938 ms.	f13
14859	 11228	14859*2^11228-1 is prime!  Time : 173.080 ms.	f13
15639	 66328	15639*2^66328-1 is prime!  Time : 11.412 sec.	f16
16431	  4198	16431*2^4198-1 is prime!  Time : 71.150 ms.	f12
17889	 10628	17889*2^10628-1 is prime!  Time : 169.037 ms.	f13
21501	  7286	21501*2^7286-1 is prime!  Time : 68.104 ms.	f12
26091	  4198	26091*2^4198-1 is prime!  Time : 25.548 ms.	f12
26511	167154	26511*2^167154-1 is prime!  Time : 124.567 sec.	f17
26601	 46246	26601*2^46246-1 is prime!  Time : 5.842 sec.	f15
30171	 76286	30171*2^76286-1 is prime!  Time : 15.664 sec.	f16
31431	 16942	31431*2^16942-1 is prime!  Time : 153.476 ms.	f14
31749	  5040	31749*2^5040-1 is prime!  Time : 35.640 ms.	f12
31959	 19704	31959*2^19704-1 is prime!  Time : 638.666 ms.	f14
35259	 10540	35259*2^10540-1 is prime!  Time : 165.366 ms.	f13
Odd n's, 31 k's remaining to be tested :

Code:
 k        2k	tested up to (n-1 base 2)

6927    13854	261944
8367    16734	262044
30003   60006	261942
39687   79374	253076
46923   93846	 50174
48927   97854	 32872
53973   107946	 33286
59655   119310	 32880
75363   150726	 65610
75873   151746	 48586
79437   158874	 32788
86613   173226	 65582
99363   198726	 65742
100377  200754	 94060
103947  207894	 47788
106377  212754	 48224
114249  228498	 33078
130383  260766	 69970
130467  260934	 68508
131727  263454	154104
133977  267954	 54508
135567  271134	 58004
144117  288234	 60384
145257  290514	121452
147687  295374	 53488
148323  296646	 53126
154317  308634	 53408
155877  311754	 58384
161583  323166	 53702
163503  327006	 53678
172167  344334	262032
Odd n's, 83 primes found / known :

Code:
Normalized	As discovered
 k         n
903	 10227	1806*2^10226-1 is prime!  Time : 467.128 ms.
2433	     3	4866*2^2-1 = 19463 is prime!
4887	  4289	9774*2^4288-1 is prime!  Time : 31.737 ms.
5007	  6765	10014*2^6764-1 is prime!  Time : 132.857 ms.
5163	  6183	10326*2^6182-1 is prime!  Time : 141.222 ms.
7977	 31265	15954*2^31264-1 is prime!  Time : 4.011 sec.
9087	  4741	18174*2^4740-1 is prime!  Time : 90.434 ms.
10113	 14535	20226*2^14534-1 is prime!  Time : 707.671 ms.
15213	 20311	30426*2^20310-1 is prime!  Time : 1.643 sec.
19377	 18677	38754*2^18676-1 is prime!  Time : 781.275 ms.
21813	  4283	43626*2^4282-1 is prime!  Time : 375.998 ms.
22863	101135	45726*2^101134-1 is prime!  Time : 45.990 sec.
25797	     1	51594-1 is prime!
27957	 21477	55914*2^21476-1 is prime!  Time : 1.678 sec.
30357	 65361	60714*2^65360-1 is prime!  Time : 18.190 sec.
32937	  8473	65874*2^8472-1 is prime!  Time : 493.300 ms.
33837	  4273	67674*2^4272-1 is prime!  Time : 165.707 ms.
34533	 32899	69066*2^32898-1 is prime!  Time : 4.595 sec.
35193	 12483	70386*2^12482-1 is prime!  Time : 743.684 ms.
37227	     1	74454-1 is prime!
44283	  4439	88566*2^4438-1 is prime!  Time : 465.176 ms.
46107	  4277	92214*2^4276-1 is prime!  Time : 465.330 ms.
52137	 26309	104274*2^26308-1 is prime!  Time : 2.757 sec.
55983	  9851	111966*2^9850-1 is prime!  Time : 714.703 ms.
56493	  6891	112986*2^6890-1 is prime!  Time : 377.827 ms.
59763	  4611	119526*2^4610-1 is prime!  Time : 486.253 ms.
60237	     1	120474-1 is prime!
60747	     1	121494-1 is prime!
61833	  4651	123666*2^4650-1 is prime!  Time : 313.346 ms.
15663	     3	31326*2^2-1 = 125303 is prime!
63153	 60295	126306*2^60294-1 is prime!  Time : 16.792 sec.
64023	 11431	128046*2^11430-1 is prime!  Time : 938.154 ms.
66087	     1	132174-1 is prime!
67737	  4437	135474*2^4436-1 is prime!  Time : 380.406 ms.
70743	 49387	141486*2^49386-1 is prime!  Time : 9.225 sec.
72327	 17125	144654*2^17124-1 is prime!  Time : 1.523 sec.
72993	 23319	145986*2^23318-1 is prime!  Time : 2.711 sec.
75093	 15371	150186*2^15370-1 is prime!  Time : 1.336 sec.
75387	  5181	150774*2^5180-1 is prime!  Time : 407.256 ms.
78933	 11443	157866*2^11442-1 is prime!  Time : 1.068 sec.
84807	  7389	169614*2^47388-1 is prime!  Time : 8.790 sec.
87735	  4551	175470*2^4550-1 is prime!  Time : 194.893 ms.
88623	 13251	177246*2^13250-1 is prime!  Time : 1.245 sec.
88743	  4619	177486*2^4618-1 is prime!  Time : 470.335 ms.
90567	  6577	181134*2^6576-1 is prime!  Time : 627.684 ms.
91671	  8795	183342*2^8794-1 is prime!  Time : 641.417 ms.
93507	  5449	187014*2^5448-1 is prime!  Time : 490.452 ms.
97323	 52207	194646*2^52206-1 is prime!  Time : 9.747 sec.
100053	 28459	200106*2^28458-1 is prime!  Time : 4.296 sec.
100353	  5147	200706*2^5146-1 is prime!  Time : 577.426 ms.
101823	  4519	203646*2^4518-1 is prime!  Time : 377.304 ms.
102993	 48975	205986*2^48974-1 is prime!  Time : 9.151 sec.
105123	  5555	210246*2^5554-1 is prime!  Time : 429.150 ms.
105837	  5913	211674*2^5912-1 is prime!  Time : 435.785 ms.
27003	     3	54006*2^2-1 = 216023 is prime!
115167	  8685	230334*2^8684-1 is prime!  Time : 355.645 ms.
117303	  4451	234606*2^4450-1 is prime!  Time : 186.024 ms.
117867	  4513	235734*2^4512-1 is prime!  Time : 188.221 ms.
120387	  5645	240774*2^5644-1 is prime!  Time : 230.829 ms.
121557	 11817	243114*2^11816-1 is prime!  Time : 594.670 ms.
129747	 18657	259494*2^18656-1 is prime!  Time : 1.299 sec.
132507	  4485	265014*2^4484-1 is prime!  Time : 187.186 ms.
133023	  9087	266046*2^9086-1 is prime!  Time : 407.860 ms.
133947	     1	267894-1 is prime!
134037	  4421	268074*2^4420-1 is prime!  Time : 186.659 ms.
142683	 22371	285366*2^22370-1 is prime!  Time : 1.966 sec.
144393	  6567	288786*2^6566-1 is prime!  Time : 252.434 ms.
144867	     1	289734-1 is prime!
144957	  6473	289914*2^6472-1 is prime!  Time : 251.359 ms.
145587	     1	291174-1 is prime!
148227	  5997	296454*2^5996-1 is prime!  Time : 235.853 ms.
148803	 25019	297606*2^25018-1 is prime!  Time : 2.232 sec.
152907	  4365	305814*2^4364-1 is prime!  Time : 186.700 ms.
154827	  9113	309654*2^9112-1 is prime!  Time : 408.607 ms.
39093	     3	78186*2^2-1 = 312743 is prime!
157383	 44059	314766*2^44058-1 is prime!  Time : 7.957 sec.
167007	  4901	334014*2^4900-1 is prime!  Time : 202.140 ms.
167997	 18705	335994*2^18704-1 is prime!  Time : 1.300 sec.
169527	  9329	339054*2^9328-1 is prime!  Time : 419.792 ms.
169743	 23791	339486*2^23790-1 is prime!  Time : 2.079 sec.
170223	  4187	340446*2^4186-1 is prime!  Time : 184.676 ms.
170733	  7307	341466*2^7306-1 is prime!  Time : 319.059 ms.
171783	  6759	343566*2^6758-1 is prime!  Time : 256.343 ms.
Regards,

Jean
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Old 2008-01-20, 06:50   #19
gd_barnes
 
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Jean,

Very good! Nice work.

I resumed testing the Sierp odd-n conjecture on 2 cores yesterday starting from n=118K. I'm now up to n=175K. I found primes on 4 more k's, all of which came in one small grouping from n=156K-170K, as follows:

50433*2^156597+1
91437*2^161615+1
61137*2^162967+1
39297*2^169495+1


This leaves 9 k's remaining!

Testing will pause at n=200K while I sieve a new file for the remaining k's.

I will request that this thread be moved over to the conjectures project shortly.

It will probably be Monday/Tuesday before I can get the project/my site updated to include the info. for this. For the time being, Karsten is keeping good track of things.


Gary
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Old 2008-01-20, 20:29   #20
Jean Penné
 
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Quote:
Originally Posted by gd_barnes View Post
Jean,

Very good! Nice work.

I resumed testing the Sierp odd-n conjecture on 2 cores yesterday starting from n=118K. I'm now up to n=175K. I found primes on 4 more k's, all of which came in one small grouping from n=156K-170K, as follows:

50433*2^156597+1
91437*2^161615+1
61137*2^162967+1
39297*2^169495+1


This leaves 9 k's remaining!

Testing will pause at n=200K while I sieve a new file for the remaining k's.

I will request that this thread be moved over to the conjectures project shortly.

It will probably be Monday/Tuesday before I can get the project/my site updated to include the info. for this. For the time being, Karsten is keeping good track of things.


Gary

Many congrats for this work, Gary, it's very encouraging!

Regards,
Jean
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Old 2008-01-20, 23:46   #21
kar_bon
 
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to Gary and Jean:

i included all data from above in the online-page (you know where).
have a look and than i can make it available for all.

karsten
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Old 2008-01-21, 07:37   #22
Jean Penné
 
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May 2004
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Quote:
Originally Posted by kar_bon View Post
to Gary and Jean:

i included all data from above in the online-page (you know where).
have a look and than i can make it available for all.

karsten
Very nice work, Karsten!

But, indeed, I cannot continue to have 32 k's reserved, I have not computer power enough for that!

For now, I will try to continue to test the -1, odd n's up to 256K base 2 ( n <= 262144), so I will now unreserve :

k = 9519 (even n's, tested now up to n = 581680, no prime...)

(This is now a top 5000 candidate!)

and for odd n's :

k = 6927, 8367, 30003, 39687, 172167 (no prime, tested as you showed).

Best Regards,
Jean
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