Prime p₀= 762215550795541697 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 118 2 58 2 28 2 28 2 124 2 (?)
a_n: 0 2 84 86 204 206 264 266 294 296 324 326 450 452
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 452
Found by: MarkRBright
db: batch=73, k=14, 82 118 58 28 28 124

SPT(16)	762214402104544943	0 14 26 66 98 140 158 186 218 246 264 306 338 378 390 404	-1148690996754
TPT(14)	762214766254490111	0 2 6 8 78 80 120 122 210 212 246 248 258 260	-784541051586
STPT(10)	762215077543776539	0 2 12 14 90 92 168 170 180 182	-473251765158
SPT(16)	762215078755127827	0 60 90 112 142 180 190 214 240 264 274 312 342 364 394 454	-472040413870
SPT(16)	762215151064496531	0 8 20 30 78 80 90 98 120 128 138 140 188 198 210 218	-399731045166
SPT(16)	762215159287182581	0 30 66 122 156 162 222 252 290 320 380 386 420 476 512 542	-391508359116
STPT(10)	762215723377586207	0 2 30 32 72 74 114 116 144 146	172582044510
STPT(10)	762215782120116977	0 2 42 44 72 74 102 104 144 146	231324575280
SPT(18)	762215892733319333	0 14 24 30 74 78 108 126 140 144 158 176 206 210 254 260 270 284	341937777636
SPT(16)	762215967044195491	0 22 42 58 70 120 150 168 172 190 220 270 282 298 318 340	416248653794
SPT(16)	762216181666741199	0 12 80 104 132 188 194 198 224 228 234 290 318 342 410 422	630871199502