## 19628Next Prime Equation

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• Oct 3, 2008
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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