Prime p₀= 2367505338630796289 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 22 2 28 2 124 2 58 2 52 2 (?)
a_n: 0 2 48 50 72 74 102 104 228 230 288 290 342 344
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: 344
Found by: Landjunge
db: batch=81, k=14, 46 22 28 124 58 52

STPT(10)	2367504182016802781	0 2 30 32 120 122 210 212 240 242	-1156613993508
STPT(10)	2367504206028908447	0 2 12 14 72 74 132 134 144 146	-1132601887842
TPT(14)	2367504235347109589	0 2 12 14 108 110 222 224 258 260 288 290 360 362	-1103283686700
SPT(16)	2367504933653848993	0 16 34 46 58 60 76 120 124 168 184 186 198 210 228 244	-404976947296
SPT(16)	2367505090312431197	0 56 60 62 116 146 156 186 200 230 240 270 324 326 330 386	-248318365092
SPT(16)	2367505166274052127	0 14 26 32 86 102 114 122 144 152 164 180 234 240 252 266	-172356744162
SPT(16)	2367506120647493237	0 12 14 32 60 114 150 224 252 326 362 416 444 462 464 476	782016696948
SPT(16)	2367506175022239127	0 22 30 64 90 112 120 144 172 196 204 226 252 286 294 316	836391442838
SPT(16)	2367506549524263803	0 8 18 60 146 174 194 210 284 300 320 348 434 476 486 494	1210893467514
TPT(14)	2367506755328862611	0 2 36 38 48 50 60 62 120 122 198 200 258 260	1416698066322
SPT(16)	2367506849224834607	0 42 50 86 104 114 132 140 156 164 182 192 210 246 254 296	1510594038318