Sierpinski/ Riesel bases 6 to 18 - Page 4

robert44444uk · 2007-01-07, 03:09

Quote:

Originally Posted by Citrix

For base 16, I found a covering set [17,13,7,241] So S/R must be less than 372827

Citrix: Note post # 19.....

Quote:

Originally Posted by robert44444uk

OK, here are values for the covering set (for 16) [17,7,13,241] repeating every 6n.

Sierpinski 66741
Riesel 33965

Still possible lower values from the covering set [7,13,19,37,73] repeating every 9n.

Regards

Robert Smith

Citrix · 2007-01-07, 06:57

For base 10, 9701 is a smaller riesel number. 10176 is not a riesel number.
and 9175 for sierpinski side.

robert44444uk · 2007-01-07, 09:07

Quote:

Originally Posted by Citrix

For base 10, 9701 is a smaller riesel number. 10176 is not a riesel number.
and 9175 for sierpinski side.

Thank you Citrix for pointing out that 9175 is a smaller Sierpinski, don't know why I did not spot it in my worksheet, it was there marked up and everything ready to transfer to my posting!

Regarding the Riesel, I rechecked my worksheet, and certainly 10176 is a Riesel [7,11,13,37] base 10. The first six values of n factor as:

1 7*14537
2 11*79*1171
3 37*275027
4 11*9250909
5 13*7433*10531
6 11*37*67*373171

Regarding your suggested value 9701, the first six factorise as follows:

1 11*8819
2 13*74623
3 7*11*17*7411
4 907*106957
5 11*5807*15187
6 1811*5356709

I agree there are no primes up to n=2000. What is your covering set?

Regards

Robert Smith

robert44444uk · 2007-01-07, 09:15

Quote:

Originally Posted by rogue

I think that it would make sense to either put up a website or make a sticky thread with the current status for each base. It is beginning to be difficult to follow this thread.

I agree, the sticky should contain simple columnar information:

Base

Lowest known Sierpinski number
Covering set
Proven? Y/N
# of remaining candidates to be checked
Who is checking?

Lowest known Riesel number
Covering set
Proven? Y/N
# of remaining candidates to be checked
Who is checking?

I am no longer a moderator, so I can't create this. Anyone up to spending a useful hour doing this? What do others think?

Regards

Robert Smith

robert44444uk · 2007-01-07, 10:02

Quote:

Originally Posted by Citrix

Robert, since you are posting the stuff for all bases, could you post the stuff for base 3 and well as base 4. I have been working on base 4 sierpinski with some 4 candidates left, I don't know about base 4 Riesel.

Citrix

The base 3 values, and their discoverers, after doing a bit of research, are:

Sierpinski 3574321403229074 [5,7,13,17,41,73,97,193,769,6481] (Jack Brennan yahoo primenumbers 2002)

Riesel 739171331147778631 [5,7,13,17,19,37,73,97,577,757,769] (Tom Masser 2004)
http://tech.groups.yahoo.com/group/p...m/message/4690

Masser, are you one and the same person?

Given that the Riesel is more than 10^2 larger, there is a chance this is not the lowest. Actually neither are proven!!

Regards

Robert

robert44444uk · 2007-01-07, 10:46

Here is a nice easy one:

Base 21, covering set [11,13,17] repeating every 4 n

Sierpinski candidate 1002, checked all smaller non trivial, only one remaining k=118 checked to n=3500

Riesel candidate 560, checked all smaller non trivial, proven, last candidate was k=64 but prime 64*21^2867-1

tnerual · 2007-01-07, 11:40

Quote:

Originally Posted by tnerual

i will give a small try at 1468*11^n+1 ...

1468*11^26258+1 is a probable prime. Time: 201.897 sec.

i don't know how to verify that it is really prime or not

i will take the 2 last sierpinski base 11 to finish it.

Quote:

Base 11:

Covering set every 6n is [3,7,19,37]. Lowest Sierpinski k is thought to be 1490. 3 ks need to be eliminated 416, 958, 1468

robert44444uk · 2007-01-07, 12:54

Base 22 is a bit more exciting:

Sierpinski 6694 [5,23,97], 15 candidates left at n=2000, actually 22 and 484 are out of the same house, so really there are only 14.

22,346,484,942,1611,1726,1908,2991,4233,5061,5128,5659,5751,6234,6462

Riesel 4461 [5,23,97] also 14 candidates left at n=2000

185,1013,1119,1335,2529,2853,3104,3426,3656,4001,4070,4118,4302,4440

I found a relatively efficient way to check to see if any of the candidates is a possible undiscovered candidate. Just run all of the numbers in a pfgw batch with the -f100 flag, over a range of 120n and pfgw will try to factorise it. Cut and paste the results into a sorter and look at the results for each candidate. I did this with the base 22 results, and therefore know that the remaining candidates are non sierpinski or riesel.

I left 19 out because it is a bit complex, and need time to look at the possible combinations.

Well done, tneural, quite a big find!!

michaf · 2007-01-07, 17:59

Make that three down:
346*22^3180+1 is prime
1726*22^2120+1 is prime
1119*22^2849-1 is prime

tnerual · 2007-01-07, 18:33

Quote:

Originally Posted by robert44444uk

Base 11:

Lowest Riesel is thought to be 4624. 12k’s still need to be eliminated. 62, 682, 862, 904, 1528, 2410, 2690, 3110, 3544, 3788, 4208, 4564.

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

michaf · 2007-01-07, 19:05

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?

2007-01-07, 06:57	#35
Citrix Jun 2003 1,579 Posts	For base 10, 9701 is a smaller riesel number. 10176 is not a riesel number. and 9175 for sierpinski side. Last fiddled with by Citrix on 2007-01-07 at 07:17

2007-01-07, 10:46	#39
robert44444uk Jun 2003 Oxford, UK 2·7·137 Posts	Base 21 Here is a nice easy one: Base 21, covering set [11,13,17] repeating every 4 n Sierpinski candidate 1002, checked all smaller non trivial, only one remaining k=118 checked to n=3500 Riesel candidate 560, checked all smaller non trivial, proven, last candidate was k=64 but prime 64*21^2867-1

2007-01-07, 12:54	#41
robert44444uk Jun 2003 Oxford, UK 2×7×137 Posts	Base 22 Base 22 is a bit more exciting: Sierpinski 6694 [5,23,97], 15 candidates left at n=2000, actually 22 and 484 are out of the same house, so really there are only 14. 22,346,484,942,1611,1726,1908,2991,4233,5061,5128,5659,5751,6234,6462 Riesel 4461 [5,23,97] also 14 candidates left at n=2000 185,1013,1119,1335,2529,2853,3104,3426,3656,4001,4070,4118,4302,4440 I found a relatively efficient way to check to see if any of the candidates is a possible undiscovered candidate. Just run all of the numbers in a pfgw batch with the -f100 flag, over a range of 120n and pfgw will try to factorise it. Cut and paste the results into a sorter and look at the results for each candidate. I did this with the base 22 results, and therefore know that the remaining candidates are non sierpinski or riesel. I left 19 out because it is a bit complex, and need time to look at the possible combinations. Well done, tneural, quite a big find!!

2007-01-07, 17:59	#42
michaf Jan 2005 737₈ Posts	Make that three down: 34622^3180+1 is prime 172622^2120+1 is prime 111922^2849-1 is prime Last fiddled with by michaf on 2007-01-07 at 18:53 Reason: 3 down*

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2007-01-07, 19:05	#44
michaf Jan 2005 737₈ Posts	Without any math skills... so excuse me if I bugger here :> base 22: 2222^n + 1 = 22^(n+1) + 1 = 122^(n+1) + 1 so, k = 1 and that one is eliminated, therefore is k=22 and 484?