Prime p₀= 3006550866221998187 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 16 2 88 2 16 2 22 2 46 2 (?)
a_n: 0 2 54 56 72 74 162 164 180 182 204 206 252 254
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: 254
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 52 16 88 16 22 46

SPT(16)	3006547784460338747	0 44 90 96 102 104 114 146 150 182 192 194 200 206 252 296	-3081761659440
STPT(10)	3006547931208888791	0 2 6 8 48 50 90 92 96 98	-2935013109396
SPT(16)	3006548667003090317	0 12 20 26 80 92 110 132 224 246 264 276 330 336 344 356	-2199218907870
TPT(14)	3006549534511958819	0 2 72 74 102 104 138 140 150 152 168 170 180 182	-1331710039368
SPT(16)	3006549623577526451	0 6 8 38 68 90 98 120 278 300 308 330 360 390 392 398	-1242644471736
SPT(16)	3006549853712248847	0 2 20 50 72 92 110 132 134 156 174 194 216 246 264 266	-1012509749340
SPT(16)	3006550942117940929	0 12 34 108 112 130 138 178 204 244 252 270 274 348 370 382	75895942742
SPT(16)	3006550979476599859	0 12 30 52 58 72 108 142 150 184 220 234 240 262 280 292	113254601672
TPT(14)	3006551052121898399	0 2 30 32 72 74 138 140 150 152 222 224 228 230	185899900212
STPT(10)	3006551100244032161	0 2 6 8 18 20 30 32 36 38	234022033974
TPT(14)	3006551277216595679	0 2 48 50 102 104 132 134 198 200 258 260 312 314	410994597492