Prime p₀= 2306729301299380421 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 166 2 70 2 4 2 58 2 10 2 (?)
a_n: 0 2 90 92 258 260 330 332 336 338 396 398 408 410
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: 410
Found by: FritzB
db: batch=81, k=14, 88 166 70 4 58 10

SPT(16)	2306728210777311781	0 6 18 52 78 102 118 126 172 180 196 220 246 280 292 298	-1090522068640
SPT(16)	2306728580438268719	0 20 62 90 98 134 162 168 194 200 228 264 272 300 342 362	-720861111702
TPT(14)	2306728629484374959	0 2 48 50 78 80 90 92 138 140 162 164 222 224	-671815005462
SPT(16)	2306728763734346683	0 18 84 88 120 156 168 184 210 226 238 274 306 310 376 394	-537565033738
SPT(16)	2306728837137772583	0 30 50 188 194 204 210 240 284 314 320 330 336 474 494 524	-464161607838
STPT(10)	2306728869137818427	0 2 30 32 42 44 54 56 84 86	-432161561994
TPT(14)	2306729378414176379	0 2 72 74 102 104 210 212 222 224 228 230 240 242	77114795958
SPT(16)	2306729708977626817	0 10 22 34 36 96 106 112 174 180 190 250 252 264 276 286	407678246396
SPT(16)	2306730341281724777	0 96 126 150 174 182 200 242 264 306 324 332 356 380 410 506	1039982344356
TPT(14)	2306730442123121849	0 2 30 32 102 104 162 164 168 170 198 200 228 230	1140823741428
STPT(10)	2306730634281459899	0 2 78 80 120 122 162 164 240 242	1332982079478