Prime p₀= 2144132919199564607 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 52 2 58 2 4 2 118 2 40 2 (?)
a_n: 0 2 30 32 84 86 144 146 150 152 270 272 312 314
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: 314
Found by: Landjunge
db: batch=80, k=14, 28 52 58 4 118 40

SPT(18)	2144132033139933701	0 2 42 60 72 116 140 152 170 198 216 228 252 296 308 326 366 368	-886059630906
TPT(14)	2144132140660979069	0 2 12 14 72 74 210 212 228 230 402 404 432 434	-778538585538
SPT(16)	2144132172355325083	0 28 70 84 130 136 184 196 228 240 288 294 340 354 396 424	-746844239524
SPT(16)	2144132238229775611	0 28 58 96 138 142 186 226 252 292 336 340 382 420 450 478	-680969788996
SPT(16)	2144132253717344249	0 14 24 32 60 80 102 128 144 170 192 212 240 248 258 272	-665482220358
SPT(16)	2144132283950621473	0 4 28 64 70 120 124 144 190 210 214 264 270 306 330 334	-635248943134
SPT(16)	2144133261195602939	0 8 12 14 30 42 44 72 110 138 140 152 168 170 174 182	341996038332
STPT(10)	2144133333437462957	0 2 42 44 72 74 102 104 144 146	414237898350
SPT(16)	2144133774569430571	0 42 46 48 82 88 90 142 366 418 420 426 460 462 466 508	855369865964
STPT(10)	2144133997735552631	0 2 6 8 48 50 90 92 96 98	1078535988024
SPT(16)	2144134089319522357	0 36 52 66 120 150 154 162 214 222 226 256 310 324 340 376	1170119957750