20080115, 20:28  #12 
May 2004
FRANCE
2^{4}×5×7 Posts 
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 (n1 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 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. Regards, Jean 
20080115, 21:39  #13 
May 2007
Kansas; USA
10219_{10} Posts 
For the Sierp oddn 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 (n1 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 20080115 at 21:50 
20080116, 08:13  #14  
May 2004
FRANCE
2^{4}×5×7 Posts 
Quote:
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 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 Jean 

20080116, 17:44  #15 
May 2007
Kansas; USA
10219_{10} Posts 
+1 oddn 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 oddn 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 
20080119, 00:00  #16 
May 2007
Kansas; USA
11·929 Posts 
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 evenn and oddn 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 
20080119, 14:44  #17 
May 2004
FRANCE
2^{4}·5·7 Posts 
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 
20080119, 17:22  #18 
May 2004
FRANCE
2^{4}·5·7 Posts 
Gathered results for 1, base 2 even and odd n's
Here are my gathered rsults for k*2^n1 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 Code:
Normalized As discovered Keller freq. k n 2181 37890 2181*2^378901 is prime! Time : 3.036 sec. f15 6549 5076 6549*2^50761 is prime! Time : 35.101 ms. f12 8181 8018 8181*2^80181 is prime! Time : 71.021 ms. f12 8961 30950 8961*2^309501 is prime! Time : 2.395 sec. f14 11379 32252 11379*2^322521 is prime! Time : 2.594 sec. f14 12849 9788 12849*2^97881 is prime! Time : 150.938 ms. f13 14859 11228 14859*2^112281 is prime! Time : 173.080 ms. f13 15639 66328 15639*2^663281 is prime! Time : 11.412 sec. f16 16431 4198 16431*2^41981 is prime! Time : 71.150 ms. f12 17889 10628 17889*2^106281 is prime! Time : 169.037 ms. f13 21501 7286 21501*2^72861 is prime! Time : 68.104 ms. f12 26091 4198 26091*2^41981 is prime! Time : 25.548 ms. f12 26511 167154 26511*2^1671541 is prime! Time : 124.567 sec. f17 26601 46246 26601*2^462461 is prime! Time : 5.842 sec. f15 30171 76286 30171*2^762861 is prime! Time : 15.664 sec. f16 31431 16942 31431*2^169421 is prime! Time : 153.476 ms. f14 31749 5040 31749*2^50401 is prime! Time : 35.640 ms. f12 31959 19704 31959*2^197041 is prime! Time : 638.666 ms. f14 35259 10540 35259*2^105401 is prime! Time : 165.366 ms. f13 Code:
k 2k tested up to (n1 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 Code:
Normalized As discovered k n 903 10227 1806*2^102261 is prime! Time : 467.128 ms. 2433 3 4866*2^21 = 19463 is prime! 4887 4289 9774*2^42881 is prime! Time : 31.737 ms. 5007 6765 10014*2^67641 is prime! Time : 132.857 ms. 5163 6183 10326*2^61821 is prime! Time : 141.222 ms. 7977 31265 15954*2^312641 is prime! Time : 4.011 sec. 9087 4741 18174*2^47401 is prime! Time : 90.434 ms. 10113 14535 20226*2^145341 is prime! Time : 707.671 ms. 15213 20311 30426*2^203101 is prime! Time : 1.643 sec. 19377 18677 38754*2^186761 is prime! Time : 781.275 ms. 21813 4283 43626*2^42821 is prime! Time : 375.998 ms. 22863 101135 45726*2^1011341 is prime! Time : 45.990 sec. 25797 1 515941 is prime! 27957 21477 55914*2^214761 is prime! Time : 1.678 sec. 30357 65361 60714*2^653601 is prime! Time : 18.190 sec. 32937 8473 65874*2^84721 is prime! Time : 493.300 ms. 33837 4273 67674*2^42721 is prime! Time : 165.707 ms. 34533 32899 69066*2^328981 is prime! Time : 4.595 sec. 35193 12483 70386*2^124821 is prime! Time : 743.684 ms. 37227 1 744541 is prime! 44283 4439 88566*2^44381 is prime! Time : 465.176 ms. 46107 4277 92214*2^42761 is prime! Time : 465.330 ms. 52137 26309 104274*2^263081 is prime! Time : 2.757 sec. 55983 9851 111966*2^98501 is prime! Time : 714.703 ms. 56493 6891 112986*2^68901 is prime! Time : 377.827 ms. 59763 4611 119526*2^46101 is prime! Time : 486.253 ms. 60237 1 1204741 is prime! 60747 1 1214941 is prime! 61833 4651 123666*2^46501 is prime! Time : 313.346 ms. 15663 3 31326*2^21 = 125303 is prime! 63153 60295 126306*2^602941 is prime! Time : 16.792 sec. 64023 11431 128046*2^114301 is prime! Time : 938.154 ms. 66087 1 1321741 is prime! 67737 4437 135474*2^44361 is prime! Time : 380.406 ms. 70743 49387 141486*2^493861 is prime! Time : 9.225 sec. 72327 17125 144654*2^171241 is prime! Time : 1.523 sec. 72993 23319 145986*2^233181 is prime! Time : 2.711 sec. 75093 15371 150186*2^153701 is prime! Time : 1.336 sec. 75387 5181 150774*2^51801 is prime! Time : 407.256 ms. 78933 11443 157866*2^114421 is prime! Time : 1.068 sec. 84807 7389 169614*2^473881 is prime! Time : 8.790 sec. 87735 4551 175470*2^45501 is prime! Time : 194.893 ms. 88623 13251 177246*2^132501 is prime! Time : 1.245 sec. 88743 4619 177486*2^46181 is prime! Time : 470.335 ms. 90567 6577 181134*2^65761 is prime! Time : 627.684 ms. 91671 8795 183342*2^87941 is prime! Time : 641.417 ms. 93507 5449 187014*2^54481 is prime! Time : 490.452 ms. 97323 52207 194646*2^522061 is prime! Time : 9.747 sec. 100053 28459 200106*2^284581 is prime! Time : 4.296 sec. 100353 5147 200706*2^51461 is prime! Time : 577.426 ms. 101823 4519 203646*2^45181 is prime! Time : 377.304 ms. 102993 48975 205986*2^489741 is prime! Time : 9.151 sec. 105123 5555 210246*2^55541 is prime! Time : 429.150 ms. 105837 5913 211674*2^59121 is prime! Time : 435.785 ms. 27003 3 54006*2^21 = 216023 is prime! 115167 8685 230334*2^86841 is prime! Time : 355.645 ms. 117303 4451 234606*2^44501 is prime! Time : 186.024 ms. 117867 4513 235734*2^45121 is prime! Time : 188.221 ms. 120387 5645 240774*2^56441 is prime! Time : 230.829 ms. 121557 11817 243114*2^118161 is prime! Time : 594.670 ms. 129747 18657 259494*2^186561 is prime! Time : 1.299 sec. 132507 4485 265014*2^44841 is prime! Time : 187.186 ms. 133023 9087 266046*2^90861 is prime! Time : 407.860 ms. 133947 1 2678941 is prime! 134037 4421 268074*2^44201 is prime! Time : 186.659 ms. 142683 22371 285366*2^223701 is prime! Time : 1.966 sec. 144393 6567 288786*2^65661 is prime! Time : 252.434 ms. 144867 1 2897341 is prime! 144957 6473 289914*2^64721 is prime! Time : 251.359 ms. 145587 1 2911741 is prime! 148227 5997 296454*2^59961 is prime! Time : 235.853 ms. 148803 25019 297606*2^250181 is prime! Time : 2.232 sec. 152907 4365 305814*2^43641 is prime! Time : 186.700 ms. 154827 9113 309654*2^91121 is prime! Time : 408.607 ms. 39093 3 78186*2^21 = 312743 is prime! 157383 44059 314766*2^440581 is prime! Time : 7.957 sec. 167007 4901 334014*2^49001 is prime! Time : 202.140 ms. 167997 18705 335994*2^187041 is prime! Time : 1.300 sec. 169527 9329 339054*2^93281 is prime! Time : 419.792 ms. 169743 23791 339486*2^237901 is prime! Time : 2.079 sec. 170223 4187 340446*2^41861 is prime! Time : 184.676 ms. 170733 7307 341466*2^73061 is prime! Time : 319.059 ms. 171783 6759 343566*2^67581 is prime! Time : 256.343 ms. Jean 
20080120, 06:50  #19 
May 2007
Kansas; USA
11×929 Posts 
Jean,
Very good! Nice work. I resumed testing the Sierp oddn 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=156K170K, 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 
20080120, 20:29  #20  
May 2004
FRANCE
2^{4}×5×7 Posts 
Quote:
Many congrats for this work, Gary, it's very encouraging! Regards, Jean 

20080120, 23:46  #21 
Mar 2006
Germany
2·3·5^{2}·19 Posts 
to Gary and Jean:
i included all data from above in the onlinepage (you know where). have a look and than i can make it available for all. karsten 
20080121, 07:37  #22  
May 2004
FRANCE
560_{10} Posts 
Quote:
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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