20091208, 14:43  #45 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11·389 Posts 
Riesel Base 707
Conjectured k = 14 Found Primes: Code:
2*707^3501 4*707^31 6*707^11 8*707^41 10*707^11 12*707^n1 Base Released 
20091208, 14:50  #46 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11·389 Posts 
Riesel Base 713
Riesel Base 713
Conjectured k = 8 Found Primes: Code:
2*713^21 4*713^11 6*713^21 
20091208, 16:05  #47  
"Robert Gerbicz"
Oct 2005
Hungary
3113_{8} Posts 
Quote:


20091208, 17:18  #48 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11·389 Posts 
Riesel Base 716
Conjectured k = 238 Found Primes: Code:
3*716^21 4*716^51 5*716^141 7*716^11 8*716^21 9*716^31 10*716^11 13*716^271 15*716^11 17*716^21 18*716^511 19*716^31 20*716^781 22*716^111 24*716^11 25*716^31 28*716^11 30*716^31 32*716^2281 33*716^11 35*716^21 37*716^391 39*716^91 42*716^11 43*716^51 44*716^41 47*716^81 48*716^11 49*716^11 50*716^21 52*716^111 54*716^441 55*716^71 57*716^51 58*716^9151 59*716^221 60*716^21 62*716^61 63*716^51 64*716^11 65*716^6701 68*716^61 69*716^261 70*716^11 72*716^11 73*716^11 74*716^61 75*716^11 77*716^21 80*716^81 82*716^11 83*716^21 84*716^21 85*716^11 87*716^61 88*716^1671 90*716^11 93*716^11 94*716^291 97*716^2651 98*716^2161 99*716^2831 102*716^31 103*716^51 104*716^41 108*716^21 110*716^1501 112*716^11 113*716^41 114*716^181 115*716^11 119*716^21 120*716^21 124*716^71 125*716^1001 127*716^11 128*716^301 129*716^11 130*716^151 132*716^31 135*716^101 137*716^21 138*716^11 139*716^11 140*716^801 142*716^971 143*716^201 145*716^31 147*716^11 148*716^11 149*716^61 150*716^41 152*716^961 153*716^11 154*716^1451 158*716^21 159*716^11 160*716^51 162*716^71 163*716^11 164*716^21 165*716^31 167*716^21 168*716^421 169*716^111 172*716^31 173*716^21 174*716^21 175*716^11 178*716^11 180*716^11 182*716^201 184*716^11 185*716^41 187*716^3131 189*716^171 192*716^21 193*716^4191 195*716^11 197*716^521 198*716^11 202*716^91 203*716^161 204*716^11 205*716^71 207*716^261 208*716^11 212*716^121 213*716^51 214*716^51 215*716^221 217*716^11 218*716^41 219*716^41 220*716^11 223*716^11 224*716^41 225*716^51 227*716^81 228*716^1311 229*716^251 230*716^161 233*716^19721 234*716^11 237*716^11 Code:
2*716^n1 29*716^n1 38*716^n1 95*716^n1 107*716^n1 109*716^n1 117*716^n1 123*716^n1 134*716^n1 179*716^n1 190*716^n1 194*716^n1 200*716^n1 Code:
1 6 11 12 14 16 21 23 26 27 31 34 36 40 41 45 46 51 53 56 61 66 67 71 76 78 79 81 86 89 91 92 96 100 101 105 106 111 116 118 121 122 126 131 133 136 141 144 146 151 155 156 157 161 166 170 171 176 177 181 183 186 188 191 196 199 201 206 209 210 211 216 221 222 226 231 232 235 236 
20091208, 17:46  #49 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11×389 Posts 
So we'd need a prime 10^(2^x)+1 that can also be expressed as 10^(3*n+1)+1, right? For that to be, 2^x needs to be 1 mod 3, which means x needs to be even. I think it's safe to say Sierp base 1000 won't be proven by finding a prime in any of our lifetimes, if ever.
Last fiddled with by TimSorbet on 20091208 at 17:56 
20091208, 18:01  #50  
"Robert Gerbicz"
Oct 2005
Hungary
3^{2}·179 Posts 
Quote:


20091208, 18:05  #51 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11·389 Posts 
Oh okay, that makes sense. I wonder why the script has a section for k's eliminated because they're equivalent to GFNs, but didn't detect k=10 as such. Perhaps it only looks for GFNs in base b, so it didn't notice that k=10 made a base 10 GFN?
Last fiddled with by gd_barnes on 20100118 at 14:34 Reason: remove base <= 500 
20091208, 19:50  #52  
"Gary"
May 2007
Overland Park, KS
7^{2}×241 Posts 
Quote:
That is there are more GFNs than just b^m*b^n+1. There's also q^m*b^n+1 where q is a perfect root of b (base). That is since 1000=10^3, then q=10, so k=10^0, 10^1, 10^2, etc. are also GFNs for base 1000. I knew this from my experience with base 32, which has GFNs for k's that are powers of 2 (instead of only 32) and completely forgot about it when I made the final modifications to the script. This shouldn't be hard to change the script. I need to add Willem as one of the main contributors in the comments anyway as well as put some sort of version in there. I'll call Karsten/Micha's original version 1.0, Willem's version 2.0, and Ian/my version 3.0. I'll then make the version with the correct for the GFNs version 3.1. Gary Last fiddled with by gd_barnes on 20100118 at 14:35 Reason: remove base <= 500 

20091208, 20:39  #53  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11×389 Posts 
Quote:
Ok good. 

20091208, 22:51  #54  
"Gary"
May 2007
Overland Park, KS
7^{2}×241 Posts 
Quote:
I noticed that one thing that makes them more rare than expected is that many of the k's that make "nonstandard" GFNs for bases are first eliminated by trivial factors and so would not get checked by the GFN routine. It is not possible for "standard" GFNs to be eliminated by trivial factors because standard GFN's can only have the factors of b and trivial k factors are based off of the factors of b1. By mathematical rule, consecutive numbers cannot have any common factors. So they become an issue immediately and clearly if you don't eliminate them ahead of time and they don't have a prime at a fairly low nvalue whereas the nonstandard ones take a while to pop their heads up in somewhat unusual situations. Edit: One more thing I just realized. I need to tweak my definition of GFN's on the web pages and the project definition in the "come join us" thread. Just another thing to do. lol Gary Last fiddled with by gd_barnes on 20091208 at 22:59 

20091212, 10:28  #55 
"Gary"
May 2007
Overland Park, KS
7^{2}×241 Posts 
Reserving Riesel and Sierp bases 512 and 1024. (4 bases)
I've already run the script against all 4 to n=2500 but it has the GFN bug so I'm going to use them for testing when I get to that. Outstide of the erroneous GFNs remaining, there's not much remaining on most of them. I've also wanted to kick start a few more powerof2 bases. 
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