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 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! :bounce: 
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 
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 
Still another one!
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... 
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. 
63411*2^72064+1 is prime! Time: 42.157 sec.

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. 
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. 
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. " 
33879*2^378022+1 is prime!
only 5 left now :smile: 
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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