mersenneforum.org Sierpinski/ Riesel bases 6 to 18
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 2007-01-07, 20:17 #45 michaf     Jan 2005 479 Posts 2 more down: 2529*22^3700-1 is prime 5751*22^4272+1 is prime
 2007-01-07, 20:54 #46 rogue     "Mark" Apr 2003 Between here and the 22×23×67 Posts These base 10 candidates are all prime 2311*10^1000+1 2607*10^780+1 2683*10^1049+1 3301*10^1228+1 3312*10^960+1 3345*10^584+1 3981*10^1239+1 4863*10^1554+1 5125*10^1597+1 5556*10^1412+1 6841*10^771+1 7459*10^978+1 7534*10^1377+1 7866*10^1854+1 8454*10^1064+1 8724*10^996+1 8922*10^1020+1 9043*10^1342+1 1506*10^872-1 3015*10^1127-1 4577*10^1145-1 5499*10^544-1 5897*10^1159-1 6633*10^1753-1 7602*10^555-1 8174*10^753-1 9461*10^579-1
 2007-01-07, 20:58 #47 tnerual     Oct 2006 7×37 Posts looking at all messages above, here are the actual work to do ... with reservation (limited) it includes all confirmed observation: base 10 maybe screwed at the end (see post 49 or 50 from citrix and the possible bug in srsieve) Code: Base 6: Sierpinski 1 to 243417 Reisel 1 to 213409 Base 7: Totally horrible. Possible covering set with repeat every 24 n is [19,5,43,1201,13,181,193,73], also 5 other sets perming 73, 193 and 409. Sierpinski and Riesel numbers are both lower than 162643669672445 Work is needed to find a low k value which is Riesel or Sierpinski. Base 8: Sierpinski 1 Riesel (done?) Base 9: Sierpinski (done ?) Riesel 4 jasong 16 36 64 Note 16 and 64 are subsets of 4. Base 10: Sierpinski 804*10^n+1 1024*10^n+1 2157*10^n+1 2661*10^n+1 4069*10^n+1 5028*10^n+1 5512*10^n+1 5565*10^n+1 6172*10^n+1 7404*10^n+1 7666*10^n+1 7809*10^n+1 8194*10^n+1 8425*10^n+1 8667*10^n+1 8889*10^n+1 9021*10^n+1 9175*10^n+1 Riesel 1343*10^n-1 1803*10^n-1 1935*10^n-1 2276*10^n-1 2333*10^n-1 3356*10^n-1 4016*10^n-1 4421*10^n-1 4478*10^n-1 6588*10^n-1 6665*10^n-1 7019*10^n-1 8579*10^n-1 9701*10^n-1 9824*10^n-1 10176*10^n-1 Base 11: Sierpinski 416 tnerual 958 tnerual Riesel 62 682 862 904 1528 2410 2690 3110 3544 3788 4208 4564 Base 12: Sierpinski 1 to 14599 Riesel 1 to 16328. Base 13: Sierpinski (done) Riesel 288 Base 14: done Base 15: Horrible. A covering set is [241,113,211,17,1489,13,3877], and Sierpinski and Riesel values are therefore less than 7330957703181619. As bad as the base 3 problem. Base 16: Sierpinski number not known, 186 (to be removed see post #49 below by citrix) 2158 (tested up to n=4000 by citrix) 2857 (tested up to n=4000 by citrix) 2908 (tested up to n=4000 by citrix) 3061 (tested up to n=4000 by citrix) 4885 (tested up to n=4000 by citrix) 5886 (tested up to n=4000 by citrix) 6348 (tested up to n=4000 by citrix) 6663 (tested up to n=4000 by citrix) 6712 (tested up to n=4000 by citrix) 7212 (tested up to n=4000 by citrix) 7258 (tested up to n=4000 by citrix) 7615 (tested up to n=4000 by citrix) 7651 (tested up to n=4000 by citrix) 7773 (tested up to n=4000 by citrix) 8025 (tested up to n=4000 by citrix) 10001 to 66740 Riesel 1343*16^n-1 1803*16^n-1 1935*16^n-1 2333*16^n-1 3015*16^n-1 3332*16^n-1 4478*16^n-1 4500*16^n-1 4577*16^n-1 5499*16^n-1 5897*16^n-1 6588*16^n-1 6633*16^n-1 6665*16^n-1 7019*16^n-1 7602*16^n-1 8174*16^n-1 8579*16^n-1 10001 to 33965 Base 17: Sierpinski 92 (LTD) 160 (LTD) 244 (LTD) 262 (LTD) Riesel (done) Base 18: Sierpinski 18 xentar 324 xentar 122 xentar 381 xentar Riesel (done) Base 19: ? Base 20: ? Base 21: Sierpinski 118 (checked to n=3500) riesel (done) Base 22: Sierpinski 22 484 942 1611 1908 2991 4233 5061 5128 5659 6234 6462 Riesel 185 1013 1335 2853 3104 3426 3656 4001 4070 4118 4302 4440 Last fiddled with by tnerual on 2007-01-07 at 21:56 Reason: with info up to post 50
 2007-01-07, 21:06 #48 rogue     "Mark" Apr 2003 Between here and the 140248 Posts I think there is a bug in srsieve (although it could be the version I have). When I input all of the base 10 candidates, it immediately removes 9701*10^n-1, but if I sieve that separately or change my input list, it is not removed. Very odd.
 2007-01-07, 21:24 #49 Citrix     Jun 2003 110001010112 Posts @ rouge, I have checked base 10 upto 2100. Here are the candidates left. 804*10^n+1 1024*10^n+1 2157*10^n+1 2661*10^n+1 4069*10^n+1 5028*10^n+1 5512*10^n+1 5565*10^n+1 6172*10^n+1 7404*10^n+1 7666*10^n+1 7809*10^n+1 8194*10^n+1 8425*10^n+1 8667*10^n+1 8889*10^n+1 9021*10^n+1 9175*10^n+1 1343*10^n-1 1803*10^n-1 1935*10^n-1 2276*10^n-1 2333*10^n-1 3356*10^n-1 4016*10^n-1 4421*10^n-1 4478*10^n-1 6588*10^n-1 6665*10^n-1 7019*10^n-1 8579*10^n-1 9461*10^n-1 Here are some primes I found. 8922*10^504+1 8454*10^509+1 3312*10^544+1 5499*10^544+-1 7602*10^555+-1 3345*10^584+1 8174*10^753+-1 6841*10^771+1 2607*10^780+1 3301*10^788+1 3345*10^866+1 1506*10^872+-1 8724*10^924+1 3312*10^960+1 7459*10^978+1 8724*10^996+1 2311*10^1000+1 8922*10^1020+1 9043*10^1034+1 6633*10^1036+-1 2683*10^1049+1 8454*10^1064+1 7459*10^978+1 3015*10^1127+-1 4577*10^1145+-1 5897*10^1159+-1 3981*10^1239+1 7534*10^1377+1 5556*10^1412+1 4863*10^1554+1 5125*10^1597+1 7866*10^1854+1 3332*10^1952+-1 2111*10^1960+-1 8953*10^2057+1 6687*10^2097+1 The last few candidates are missing. Once srsieve removed 9701 from the sieve I assumed it was sierpinski and removed the ones after that from the sieve. same on the riesel side. You can continue on base 10. I will not work on it. Also for base 16. looking on prothsearch.net 93*2^586453+1 is prime. This removes 186. On riesel side 225*2^9005-1 is prime. So 450 is removed. Last fiddled with by Citrix on 2007-01-07 at 21:41
 2007-01-07, 21:54 #50 tnerual     Oct 2006 7×37 Posts is there any application where i can enter the base (fixed), a range of k and then a starting n. then start the app. the app must remove (and log) all prime k for n then test all remaining k for primality at the next n and so on. i'm sure there is something like that but i don't know what. citrix i think you use that (looking at your 10000 k range on base 16, you can't do it manually )
2007-01-07, 22:09   #51
Citrix

Jun 2003

157910 Posts

Quote:
 Originally Posted by tnerual citrix i think you use that (looking at your 10000 k range on base 16, you can't do it manually )
I wrote a program for myself for the low n's. Then I used srsieve and PFGW for high n and removed candidates manually.

 2007-01-08, 03:27 #52 rogue     "Mark" Apr 2003 Between here and the 22×23×67 Posts Here are more base 10 primes: 2276*10^2726-1 2333*10^2113-1 4016*10^3647-1 4478*10^4817-1 6588*10^7442-1 9701*10^6538-1 9824*10^1857-1 1024*10^4554+1 2157*10^3560+1 2661*10^2681+1 5512*10^3004+1 5565*10^3175+1 804*10^7558+1 8425*10^3661+1 8667*10^6617+1 8889*10^7588+1 9021*10^8090+1 The remaining in base 10 are: 4069*10^n+1 5028*10^n+1 6172*10^n+1 7404*10^n+1 7666*10^n+1 7809*10^n+1 8194*10^n+1 1343*10^n-1 1803*10^n-1 1935*10^n-1 3356*10^n-1 4421*10^n-1 6665*10^n-1 7019*10^n-1 8579*10^n-1 I'll continue on these for a while. Last fiddled with by rogue on 2007-01-08 at 03:31
2007-01-08, 06:37   #53
robert44444uk

Jun 2003
Oxford, UK

2·7·137 Posts

Quote:
 Originally Posted by michaf Without any math skills... so excuse me if I bugger here :> base 22: 22*22^n + 1 = 22^(n+1) + 1 = 1*22^(n+1) + 1 so, k = 1 and that one is eliminated, therefore is k=22 and 484?
Unfortunately not. 1*22^1+1=23 prime, but, I think we decided for the Sierpinski base 5 exercise, that we would not use n=0, otherwise k=22 could be eliminated but not 484.

2007-01-08, 06:39   #54
robert44444uk

Jun 2003
Oxford, UK

35768 Posts
Base 16

Quote:
 Originally Posted by Citrix Also for base 16. looking on prothsearch.net 93*2^586453+1 is prime. This removes 186. On riesel side 225*2^9005-1 is prime. So 450 is removed.
Brilliant, it is worth checking the top 5000 and prothsearch from time to time!

Last fiddled with by robert44444uk on 2007-01-08 at 06:49

2007-01-08, 06:47   #55
robert44444uk

Jun 2003
Oxford, UK

2×7×137 Posts
Base 11

Quote:
 Originally Posted by tnerual what do you think of 416*11^n-1 in 5 seconds i can find all factors for n=1 to n=50000000 maybe it's a lowest riesel ... if it is i'm lucky/stupid (confusion between -1 and +1 with 416 one of the two last k in sierpinski side) LAurent
Unfortunately it is a trivial case, all n are divisible by 5.

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