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19628Next Prime Equation

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  • Sebastian Martin
    Oct 3, 2008
    • 0 Attachment
      Hello all:

      Next Prime Equation:

      Let p a prime number, consider the following equation:

      1+z*(p!!)-x*p-x-x*y = 0

      Let (x,y,z) a solution in positive integers. x,y,z >=1

      If y is minimun then p+1+y=q is the next prime number for p. (and exist this minimum)


      MATHEMATICA EXAMPLE:

      F[n_,x_,y_,z_]:=1+z*Prime[n]!!-x*Prime[n]-x-x*y

      Prime[4]=7

      Do[If[F[n,x,y,z]0,Print[Prime[n]+1+y," ",{x,y,z}," ",x+y+z]],{x,1,300},{y,1,300},{z,1,300},{n,4,4}]
      106 {1,98,1} 100
      211 {1,203,2} 206
      53 {2,45,1} 48
      158 {2,150,3} 155
      263 {2,255,5} 262
      79 {4,71,3} 78
      184 {4,176,7} 187
      289 {4,281,11} 296
      92 {8,84,7} 99
      197 {8,189,15} 212
      302 {8,294,23} 325
      86 {11,78,9} 98
      191 {11,183,20} 214
      296 {11,288,31} 330
      97 {13,89,12} 114
      202 {13,194,25} 232
      307 {13,299,38} 350
      46 {16,38,7} 61
      151 {16,143,23} 182
      256 {16,248,39} 303
      68 {17,60,11} 88
      173 {17,165,28} 210
      278 {17,270,45} 332
      94 {19,86,17} 122
      199 {19,191,36} 246
      304 {19,296,55} 370
      43 {22,35,9} 66
      148 {22,140,31} 193
      253 {22,245,53} 320
      32 {23,24,7} 54
      137 {23,129,30} 182
      242 {23,234,53} 310
      101 {26,93,25} 144
      206 {26,198,51} 275
      29 {29,21,8} 58
      134 {29,126,37} 192
      239 {29,231,66} 326
      61 {31,53,18} 102
      166 {31,158,49} 238
      271 {31,263,80} 374
      23 {32,15,7} 54
      128 {32,120,39} 191
      233 {32,225,71} 328
      34 {34,26,11} 71
      139 {34,131,45} 210
      244 {34,236,79} 349
      88 {37,80,31} 148
      193 {37,185,68} 290
      298 {37,290,105} 432
      47 {38,39,17} 94
      152 {38,144,55} 237
      257 {38,249,93} 380
      41 {41,33,16} 90
      146 {41,138,57} 236
      251 {41,243,98} 382
      22 {43,14,9} 66
      127 {43,119,52} 214
      232 {43,224,95} 362
      74 {44,66,31} 141
      179 {44,171,75} 290
      284 {44,276,119} 439
      16 {46,8,7} 61
      121 {46,113,53} 212
      226 {46,218,99} 363
      38 {47,30,17} 94
      143 {47,135,64} 246
      248 {47,240,111} 398
      103 {52,95,51} 198
      208 {52,200,103} 355
      107 {53,99,54} 206
      212 {53,204,107} 364
      67 {58,59,37} 154
      172 {58,164,95} 317
      277 {58,269,153} 480
      89 {59,81,50} 190
      194 {59,186,109} 354
      299 {59,291,168} 518
      31 {61,23,18} 102
      136 {61,128,79} 268
      241 {61,233,140} 434
      83 {62,75,49} 186
      188 {62,180,111} 353
      293 {62,285,173} 520
      64 {64,56,39} 159
      169 {64,161,103} 328
      274 {64,266,167} 497
      58 {67,50,37} 154
      163 {67,155,104} 326
      268 {67,260,171} 498
      17 {68,9,11} 88
      122 {68,114,79} 261
      227 {68,219,147} 434
      71 {71,63,48} 182
      176 {71,168,119} 358
      281 {71,273,190} 534
      82 {73,74,57} 204
      187 {73,179,130} 382
      292 {73,284,203} 560
      44 {74,36,31} 141
      149 {74,141,105} 320
      254 {74,246,179} 499
      76 {76,68,55} 199
      181 {76,173,131} 380
      286 {76,278,207} 561
      109 {79,101,82} 262
      214 {79,206,161} 446
      73 {82,65,57} 204
      178 {82,170,139} 391
      283 {82,275,221} 578
      62 {83,54,49} 186
      167 {83,159,132} 374
      272 {83,264,215} 562
      11 {86,3,9} 98 (*** y=3 minimun; nextPrime=11 ******)
      116 {86,108,95} 289
      221 {86,213,181} 480
      37 {88,29,31} 148
      142 {88,134,119} 341
      247 {88,239,207} 534
      59 {89,51,50} 190
      164 {89,156,139} 384
      269 {89,261,228} 578
      113 {92,105,99} 296
      218 {92,210,191} 493
      19 {94,11,17} 122
      124 {94,116,111} 321
      229 {94,221,205} 520
      13 {97,5,12} 114
      118 {97,110,109} 316
      223 {97,215,206} 518
      26 {101,18,25} 144
      131 {101,123,126} 350
      236 {101,228,227} 556





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