Prime p₀= 2373499307859662657 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 28 2 76 2 28 2 70 2 28 2 (?)
a_n: 0 2 24 26 54 56 132 134 162 164 234 236 264 266
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: 266
Found by: Landjunge
db: batch=81, k=14, 22 28 76 28 70 28

SPT(16)	2373498101069705963	0 38 56 66 84 86 150 218 246 314 378 380 398 408 426 464	-1206789956694
SPT(16)	2373498585528074429	0 12 42 68 78 104 120 152 210 242 258 284 294 320 350 362	-722331588228
STPT(10)	2373498629787125567	0 2 24 26 42 44 60 62 84 86	-678072537090
SPT(16)	2373498732271422017	0 44 54 86 96 146 224 230 246 252 330 380 390 422 432 476	-575588240640
SPT(16)	2373499088784199351	0 6 42 82 108 150 166 178 180 192 208 250 276 316 352 358	-219075463306
SPT(16)	2373499195905834859	0 22 48 52 150 172 192 244 288 340 360 382 480 484 510 532	-111953827798
SPT(16)	2373499423078526453	0 36 68 78 110 126 168 198 266 296 338 354 386 396 428 464	115218863796
STPT(10)	2373499775515383167	0 2 42 44 102 104 162 164 204 206	467655720510
STPT(10)	2373499803195000437	0 2 12 14 42 44 72 74 84 86	495335337780
SPT(16)	2373500306496149839	0 10 12 28 52 72 78 88 162 172 178 198 222 238 240 250	998636487182
SPT(16)	2373500327405448053	0 14 30 54 74 134 140 158 180 198 204 264 284 308 324 338	1019545785396