Prime p₀= 2157398150225404349 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 112 2 94 2 10 2 58 2 10 2 (?)
a_n: 0 2 18 20 132 134 228 230 240 242 300 302 312 314
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=81, k=14, 16 112 94 10 58 10

SPT(16)	2157396631979809237	0 10 40 70 72 94 96 154 162 220 222 244 246 276 306 316	-1518245595112
SPT(16)	2157396925584486431	0 6 42 68 126 132 138 140 228 230 236 242 300 326 362 368	-1224640917918
SPT(16)	2157396935915605589	0 2 8 50 78 98 102 132 200 230 234 254 282 324 330 332	-1214309798760
SPT(16)	2157396950494062427	0 10 30 34 52 54 120 132 184 196 262 264 282 286 306 316	-1199731341922
SPT(16)	2157397447357427459	0 38 44 90 114 134 150 158 174 182 198 218 242 288 294 332	-702867976890
STPT(10)	2157398073698181707	0 2 30 32 42 44 54 56 84 86	-76527222642
SPT(16)	2157398170217759923	0 16 18 60 70 100 130 168 268 306 336 366 376 418 420 436	19992355574
STPT(10)	2157398975311171619	0 2 18 20 30 32 42 44 60 62	825085767270
SPT(16)	2157399246454229003	0 24 74 90 98 140 156 186 188 218 234 276 284 300 350 374	1096228824654
SPT(16)	2157399349306902409	0 4 18 102 108 132 144 174 238 268 280 304 310 394 408 412	1199081498060
SPT(16)	2157399714333491107	0 22 30 60 76 102 126 154 162 190 214 240 256 286 294 316	1564108086758