Sierpinski base 4

Citrix · 2005-01-27, 03:52

I have a slow computer that won't be of much help to the PSP project, so I am working on this problem on that computer. If anyone has any computers that won't be of much help to PSP can consider to help with this

66741 is the smallest number (k) that is a multiple of 3 and k*4^n+1 is never prime!

THe following k and n are left: (20), Please eliminate. Use Newpgen and LLR 3.5. Remember to enter base 4 than 2.
Post below to reserve a k. The aim is to take all the k's to 100,000 and then stop.

Scores
Mark 3
Footmaster 3
Citrix 0
Jean Penne 1
Mystwalker 1
masser 1

k Upper limit Relative weight Reserved by
5886 10000 92 Citrix
8139 10000 86 Citrix
18534 50000 80 Citrix
23451 46000 332 Mystwalker
23799 10000 268
33771 10000 142 Jean Penne
33879 20000 716 Mystwalker
34914 10000 455
35874 10000 448
41709 10000 410 Geoff
42717 10000 622 Geoff
49386 10000 319
51171 10000 731 masser
53226 10000 177 Carlos
55611 20000 536
60849 10000 387
60891 10000 275
63411 10000 316
64494 10000 272 Keller
66741 Sierpinski number for base 4

9 primes found so far!
15441*2^20584+1 is prime! Time: 1.172 sec. by Footmaster
21069*2^23006+1 is prime! Time: 1.751 sec. by Footmaster
21699*2^72874+1 is prime! Time: 21.318 sec. by Footmaster
14661*2^91368+1 is prime! Time: 42.331 sec. by Jean Penne
58791*2^79420+1 is prime! Time: 27.092 sec. by Mystwalker
52839*2^32558+1 is prime! Time: 2.640 sec. by masser
50166*4^12490+1 is prime! by Mark
45306*4^14484+1 is prime! by Mark
30579*4^24297+1 is prime! by Mark

Have fun eliminating these!

Jean Penné · 2005-01-27, 14:52

I wish to ask some questions about the choose you made of the candidate
k values :

let N = k*4^n +1 with k odd.

I wish to compute N modulo 3.

4 = 1 (mod 3), so 4^n = 1 (mod 3)

so, N = k+1 (mod 3) All the possibilities are here :

k = 0 (mod 3) ==> N = 1 (mod 3)
k = 1 (mod 3) ==> N = 2 (mod 3)
k = 2 (mod 3) ==> N = 0 (mod 3), so these k's are all Sierpinski base 4 !!

Without any restriction on the k values, the "Sierpinski base 4" problem
would be rather trivial, because the least Sierpinki would be k = 5!

( I verified that with Newpgen...)

So, I understand why you added the condition 3 | k in your definition...
But why do you also exclude k = 1 (mod 3) ? Perhaps to avoid the values
already taken by Seventeen or Bust project, am I wrong ?

Regards,
Jean

Citrix · 2005-01-29, 16:52

Here is the updated tables so far!

Open:
k Upper limit Relative weight
49386 10000 319
60849 10000 387
63411 10000 316
42717 100000 622

Reservations:
5886 Citrix
8139 Citrix
18534 Citrix
23451 Mystwalker (on hold...see message 46 for newpgen files)
33771 Jean Penne
33879 Mystwalker (on hold...see message 46 for newpgen files)
51171 masser
64494 Keller

Primes:
15441*4^10292+1 is prime! Footmaster
21069*4^11503+1 is prime! Footmaster
21699*4^36437+1 is prime! Footmaster
14661*4^45684+1 is prime! Jean Penne
58791*4^39710+1 is prime! Mystwalker
52839*4^16279+1 is prime! masser
50166*4^12490+1 is prime! Mark
45306*4^14484+1 is prime! Mark
30579*4^24297+1 is prime! Mark
35874*4^26963+1 is prime! tcadigan
34914*4^14781+1 is prime! tcadigan
53226*4^44874+1 is prime! em99010pepe
41709*4^40297+1 is prime! geoff
60891*2^40144+1 is prime! Jean Penne
55611*4^20106+1 is prime! Citrix
23799*4^52945+1 is prime! Ken_g6

Scores:
em99010pepe 1
Footmaster 3
Jean Penne 2
Mark 3
masser 1
Mystwalker 1
tcadigan 2
Geoff 1
Ken_g6 1
Citrix 1

12 k's left

Jean Penné · 2005-01-29, 19:10

33771*4^89100+1 = 33771*2^178200+1 is prime! Time: 183.245 sec.

I think we enter now in the top 5000 !

I wish to reserve k = 42717 and continue it...

Citrix · 2005-01-31, 16:57

k Upper limit Relative weight Reserved by
5886 50000 92 Citrix
8139 10000 86 Citrix
18534 50000 80 Citrix
33879 30000 716 Mystwalker
42717 100000 622 Jean Penne
49386 10000 319 Footmaster
60849 10000 387 masser
63411 10000 316 Footmaster
23451 60000 332 Mystwalker
64494 10000 272 Keller
66741 Sierpinski number for base 4

10 k's left

Top 5000 primes
33771*2^178200+1 is prime! Time: 183.245 sec.
51171*2^184528+1 is prime! Time: 87.521 sec.

Footmaster · 2005-01-31, 17:05

63411*2^72064+1 is prime! Time: 42.157 sec.

Citrix · 2005-02-01, 00:16

k Upper limit Relative weight Reserved by
5886 50000 92 Citrix
8139 10000 86 Citrix
18534 50000 80 Citrix
33879 30000 716 Mystwalker
42717 100000 622 Jean Penne
49386 10000 319 Footmaster
60849 10000 387 masser
23451 60000 332 Mystwalker
64494 10000 272 Keller
66741 Sierpinski number for base 4

9 k's left

Top 5000 primes
33771*2^178200+1 is prime! Time: 183.245 sec.
51171*2^184528+1 is prime! Time: 87.521 sec.

Citrix · 2005-02-01, 05:08

8139*4^12977+1 is prime!

k Upper limit Relative weight Reserved by
5886 50000 92 Citrix
18534 57750 80 Citrix
33879 30000 716 Mystwalker
42717 100000 622 Jean Penne
49386 10000 319 Footmaster
60849 10000 387 masser
23451 60000 332 Mystwalker
64494 10000 272 Keller
66741 Sierpinski number for base 4

8 k's left

Top 5000 primes
33771*2^178200+1 is prime! Time: 183.245 sec.
51171*2^184528+1 is prime! Time: 87.521 sec.

Footmaster · 2005-05-25, 06:44

49386*2^357416+1 is Prime!

I'll like to take 60849 next.

See if I get lucky with this one.

Regards

Foots

PS. When I submitted it it at prime pages it said this:
"The description "49386*2^357416+1" was modified to "24693*2^357417+1" in accordance with our canonicalization procedures. "

Footmaster · 2005-06-20, 10:21

33879*2^378022+1 is prime!

only 5 left now

Jean Penné · 2005-11-05, 16:11

Going back from a trip in Viet Nam and Cambodia, I found this on my P4 :

42717*2^905792+1 is prime! Time: 7292.117 sec.

So, now, only 4 k's remain to be eliminated !

This is very encouraging, so, I wish now to take k = 23451

Happy hunting to all,

Jean

2005-01-27, 03:52	#1
Citrix Jun 2003 2²×397 Posts	Sierpinski base 4 I have a slow computer that won't be of much help to the PSP project, so I am working on this problem on that computer. If anyone has any computers that won't be of much help to PSP can consider to help with this 66741 is the smallest number (k) that is a multiple of 3 and k4^n+1 is never prime! THe following k and n are left: (20), Please eliminate. Use Newpgen and LLR 3.5. Remember to enter base 4 than 2. Post below to reserve a k. The aim is to take all the k's to 100,000 and then stop. Scores Mark 3 Footmaster 3 Citrix 0 Jean Penne 1 Mystwalker 1 masser 1 k Upper limit Relative weight Reserved by 5886 10000 92 Citrix 8139 10000 86 Citrix 18534 50000 80 Citrix 23451 46000 332 Mystwalker 23799 10000 268 33771 10000 142 Jean Penne 33879 20000 716 Mystwalker 34914 10000 455 35874 10000 448 41709 10000 410 Geoff 42717 10000 622 Geoff 49386 10000 319 51171 10000 731 masser 53226 10000 177 Carlos 55611 20000 536 60849 10000 387 60891 10000 275 63411 10000 316 64494 10000 272 Keller 66741 Sierpinski number for base 4 9 primes found so far! 154412^20584+1 is prime! Time: 1.172 sec. by Footmaster 210692^23006+1 is prime! Time: 1.751 sec. by Footmaster 216992^72874+1 is prime! Time: 21.318 sec. by Footmaster 146612^91368+1 is prime! Time: 42.331 sec. by Jean Penne 587912^79420+1 is prime! Time: 27.092 sec. by Mystwalker 528392^32558+1 is prime! Time: 2.640 sec. by masser 501664^12490+1 is prime! by Mark 453064^14484+1 is prime! by Mark 305794^24297+1 is prime! by Mark Have fun eliminating these! Last fiddled with by Citrix on 2005-01-27 at 23:22

2005-01-27, 14:52	#2
Jean Penné May 2004 FRANCE 2·5·59 Posts	How did you choose the candidate k values ? I wish to ask some questions about the choose you made of the candidate k values : let N = k*4^n +1 with k odd. I wish to compute N modulo 3. 4 = 1 (mod 3), so 4^n = 1 (mod 3) so, N = k+1 (mod 3) All the possibilities are here : k = 0 (mod 3) ==> N = 1 (mod 3) k = 1 (mod 3) ==> N = 2 (mod 3) k = 2 (mod 3) ==> N = 0 (mod 3), so these k's are all Sierpinski base 4 !! Without any restriction on the k values, the "Sierpinski base 4" problem would be rather trivial, because the least Sierpinki would be k = 5! ( I verified that with Newpgen...) So, I understand why you added the condition 3 \| k in your definition... But why do you also exclude k = 1 (mod 3) ? Perhaps to avoid the values already taken by Seventeen or Bust project, am I wrong ? Regards, Jean

2005-01-29, 16:52	#3
Citrix Jun 2003 2²·397 Posts	Here is the updated tables so far! Open: k Upper limit Relative weight 49386 10000 319 60849 10000 387 63411 10000 316 42717 100000 622 Reservations: 5886 Citrix 8139 Citrix 18534 Citrix 23451 Mystwalker (on hold...see message 46 for newpgen files) 33771 Jean Penne 33879 Mystwalker (on hold...see message 46 for newpgen files) 51171 masser 64494 Keller Primes: 154414^10292+1 is prime! Footmaster 210694^11503+1 is prime! Footmaster 216994^36437+1 is prime! Footmaster 146614^45684+1 is prime! Jean Penne 587914^39710+1 is prime! Mystwalker 528394^16279+1 is prime! masser 501664^12490+1 is prime! Mark 453064^14484+1 is prime! Mark 305794^24297+1 is prime! Mark 358744^26963+1 is prime! tcadigan 349144^14781+1 is prime! tcadigan 532264^44874+1 is prime! em99010pepe 417094^40297+1 is prime! geoff 608912^40144+1 is prime! Jean Penne 556114^20106+1 is prime! Citrix 237994^52945+1 is prime! Ken_g6 Scores: em99010pepe 1 Footmaster 3 Jean Penne 2 Mark 3 masser 1 Mystwalker 1 tcadigan 2 Geoff 1 Ken_g6 1 Citrix 1 12 k's left Last fiddled with by Citrix on 2005-01-29 at 17:04

2005-01-29, 19:10	#4
Jean Penné May 2004 FRANCE 2·5·59 Posts	Still another one! 337714^89100+1 = 337712^178200+1 is prime! Time: 183.245 sec. I think we enter now in the top 5000 ! I wish to reserve k = 42717 and continue it...

2005-05-25, 06:44	#9
Footmaster Mar 2004 3×13 Posts	493862^357416+1 is Prime! I'll like to take 60849 next. See if I get lucky with this one. Regards Foots PS. When I submitted it it at prime pages it said this: "The description "493862^357416+1" was modified to "246932^357417+1" in accordance with our canonicalization procedures. " Last fiddled with by Footmaster on 2005-05-25 at 06:59*

2005-01-31, 16:57	#5
Citrix Jun 2003 2²×397 Posts	k Upper limit Relative weight Reserved by 5886 50000 92 Citrix 8139 10000 86 Citrix 18534 50000 80 Citrix 33879 30000 716 Mystwalker 42717 100000 622 Jean Penne 49386 10000 319 Footmaster 60849 10000 387 masser 63411 10000 316 Footmaster 23451 60000 332 Mystwalker 64494 10000 272 Keller 66741 Sierpinski number for base 4 10 k's left Top 5000 primes 337712^178200+1 is prime! Time: 183.245 sec. 511712^184528+1 is prime! Time: 87.521 sec.

2005-01-31, 17:05	#6
Footmaster Mar 2004 3·13 Posts	63411*2^72064+1 is prime! Time: 42.157 sec.

2005-02-01, 00:16	#7
Citrix Jun 2003 2²·397 Posts	k Upper limit Relative weight Reserved by 5886 50000 92 Citrix 8139 10000 86 Citrix 18534 50000 80 Citrix 33879 30000 716 Mystwalker 42717 100000 622 Jean Penne 49386 10000 319 Footmaster 60849 10000 387 masser 23451 60000 332 Mystwalker 64494 10000 272 Keller 66741 Sierpinski number for base 4 9 k's left Top 5000 primes 337712^178200+1 is prime! Time: 183.245 sec. 511712^184528+1 is prime! Time: 87.521 sec.

2005-02-01, 05:08	#8
Citrix Jun 2003 11000110100₂ Posts	81394^12977+1 is prime! k Upper limit Relative weight Reserved by 5886 50000 92 Citrix 18534 57750 80 Citrix 33879 30000 716 Mystwalker 42717 100000 622 Jean Penne 49386 10000 319 Footmaster 60849 10000 387 masser 23451 60000 332 Mystwalker 64494 10000 272 Keller 66741 Sierpinski number for base 4 8 k's left Top 5000 primes 337712^178200+1 is prime! Time: 183.245 sec. 51171*2^184528+1 is prime! Time: 87.521 sec.

2005-06-20, 10:21	#10
Footmaster Mar 2004 3·13 Posts	33879*2^378022+1 is prime! only 5 left now

2005-11-05, 16:11	#11
Jean Penné May 2004 FRANCE 1001001110₂ Posts	k = 42717 is over ! Going back from a trip in Viet Nam and Cambodia, I found this on my P4 : 42717*2^905792+1 is prime! Time: 7292.117 sec. So, now, only 4 k's remain to be eliminated ! This is very encouraging, so, I wish now to take k = 23451 Happy hunting to all, Jean

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