Prime p₀= 2394122663638853309 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 76 2 16 2 58 2 118 2 28 2 (?)
a_n: 0 2 42 44 120 122 138 140 198 200 318 320 348 350
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: 350
Found by: Landjunge
db: batch=81, k=14, 40 76 16 58 118 28

SPT(16)	2394121621813702493	0 20 26 30 96 104 114 150 254 290 300 308 374 378 384 404	-1041825150816
SPT(16)	2394121745023576019	0 8 50 60 78 102 128 134 138 144 170 194 212 222 264 272	-918615277290
STPT(10)	2394122052472087547	0 2 30 32 42 44 54 56 84 86	-611166765762
STPT(10)	2394122336229953471	0 2 6 8 18 20 30 32 36 38	-327408899838
STPT(10)	2394122473666195037	0 2 54 56 132 134 210 212 264 266	-189972658272
STPT(10)	2394122592089044181	0 2 30 32 78 80 126 128 156 158	-71549809128
SPT(16)	2394123705204405617	0 44 62 72 80 86 114 146 150 182 210 216 224 234 252 296	1041565552308
SPT(16)	2394123883625133743	0 14 24 30 54 56 66 68 186 188 198 200 224 230 240 254	1219986280434
SPT(16)	2394123980931575821	0 10 52 66 102 108 132 136 162 166 190 196 232 246 288 298	1317292722512
SPT(16)	2394124042716719893	0 4 28 40 136 138 156 238 336 418 436 438 534 546 570 574	1379077866584
STPT(10)	2394124197638597777	0 2 90 92 132 134 174 176 264 266	1533999744468