Sierpinski/ Riesel bases 6 to 18 - Page 5

michaf · 2007-01-07, 20:17

2 more down:

2529*22^3700-1 is prime
5751*22^4272+1 is prime

rogue · 2007-01-07, 20:54

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

tnerual · 2007-01-07, 20:58

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

rogue · 2007-01-07, 21:06

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.

Citrix · 2007-01-07, 21:24

@ 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.

tnerual · 2007-01-07, 21:54

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

)

Citrix · 2007-01-07, 22:09

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.

rogue · 2007-01-08, 03:27

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.

robert44444uk · 2007-01-08, 06:37

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.

robert44444uk · 2007-01-08, 06:39

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!

robert44444uk · 2007-01-08, 06:47

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.

2007-01-08, 03:27	#52
rogue "Mark" Apr 2003 Between here and the 1100011010000₂ Posts	Here are more base 10 primes: 227610^2726-1 233310^2113-1 401610^3647-1 447810^4817-1 658810^7442-1 970110^6538-1 982410^1857-1 102410^4554+1 215710^3560+1 266110^2681+1 551210^3004+1 556510^3175+1 80410^7558+1 842510^3661+1 866710^6617+1 888910^7588+1 902110^8090+1 The remaining in base 10 are: 406910^n+1 502810^n+1 617210^n+1 740410^n+1 766610^n+1 780910^n+1 819410^n+1 134310^n-1 180310^n-1 193510^n-1 335610^n-1 442110^n-1 666510^n-1 701910^n-1 857910^n-1 I'll continue on these for a while. Last fiddled with by rogue on 2007-01-08 at 03:31

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2007-01-07, 20:17	#45
michaf Jan 2005 111011111₂ Posts	2 more down: 252922^3700-1 is prime 575122^4272+1 is prime

2007-01-07, 20:54	#46
rogue "Mark" Apr 2003 Between here and the 2⁴×397 Posts	These base 10 candidates are all prime 231110^1000+1 260710^780+1 268310^1049+1 330110^1228+1 331210^960+1 334510^584+1 398110^1239+1 486310^1554+1 512510^1597+1 555610^1412+1 684110^771+1 745910^978+1 753410^1377+1 786610^1854+1 845410^1064+1 872410^996+1 892210^1020+1 904310^1342+1 150610^872-1 301510^1127-1 457710^1145-1 549910^544-1 589710^1159-1 663310^1753-1 760210^555-1 817410^753-1 9461*10^579-1

2007-01-07, 21:06	#48
rogue "Mark" Apr 2003 Between here and the 2⁴×397 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 11000101110₂ Posts	@ rouge, I have checked base 10 upto 2100. Here are the candidates left. 80410^n+1 102410^n+1 215710^n+1 266110^n+1 406910^n+1 502810^n+1 551210^n+1 556510^n+1 617210^n+1 740410^n+1 766610^n+1 780910^n+1 819410^n+1 842510^n+1 866710^n+1 888910^n+1 902110^n+1 917510^n+1 134310^n-1 180310^n-1 193510^n-1 227610^n-1 233310^n-1 335610^n-1 401610^n-1 442110^n-1 447810^n-1 658810^n-1 666510^n-1 701910^n-1 857910^n-1 946110^n-1 Here are some primes I found. 892210^504+1 845410^509+1 331210^544+1 549910^544+-1 760210^555+-1 334510^584+1 817410^753+-1 684110^771+1 260710^780+1 330110^788+1 334510^866+1 150610^872+-1 872410^924+1 331210^960+1 745910^978+1 872410^996+1 231110^1000+1 892210^1020+1 904310^1034+1 663310^1036+-1 268310^1049+1 845410^1064+1 745910^978+1 301510^1127+-1 457710^1145+-1 589710^1159+-1 398110^1239+1 753410^1377+1 555610^1412+1 486310^1554+1 512510^1597+1 786610^1854+1 333210^1952+-1 211110^1960+-1 895310^2057+1 668710^2097+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 932^586453+1 is prime. This removes 186. On riesel side 2252^9005-1 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 )