Prime p₀= 2318872527599247251 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 124 2 28 2 22 2 16 2 10 2 (?)
a_n: 0 2 30 32 156 158 186 188 210 212 228 230 240 242
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: 242
Found by: wadesworld18
db: batch=81, k=14, 28 124 28 22 16 10

SPT(16)	2318870636050094167	0 6 12 40 42 60 82 90 136 144 166 184 186 214 220 226	-1891549153084
SPT(16)	2318871278915753747	0 56 104 122 146 170 174 180 206 212 216 240 264 282 330 386	-1248683493504
SPT(16)	2318871454778102929	0 52 70 90 118 124 150 162 220 232 258 264 292 312 330 382	-1072821144322
SPT(16)	2318871703422803387	0 20 56 60 102 110 122 144 182 204 216 224 266 270 306 326	-824176443864
SPT(16)	2318872171524610733	0 20 38 66 114 126 140 194 210 264 278 290 338 366 384 404	-356074636518
SPT(18)	2318872491373607761	0 12 22 30 78 88 100 102 120 148 166 168 180 190 238 246 256 268	-36225639490
SPT(18)	2318872545386725379	0 8 38 50 72 74 90 98 134 198 234 242 258 260 282 294 324 332	17787478128
STPT(10)	2318872665974723357	0 2 42 44 72 74 102 104 144 146	138375476106
SPT(16)	2318872737385691761	0 16 28 66 120 126 148 226 240 318 340 346 400 438 450 466	209786444510
SPT(16)	2318873058257899271	0 8 38 86 90 120 146 162 176 192 218 248 252 300 330 338	530658652020
STPT(12)	2318873115065477249	0 2 30 32 42 44 168 170 180 182 210 212	587466229998