Prime p₀= 1022687431730670131 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 274 2 10 2 40 2 4 2 40 2 (?)
a_n: 0 2 60 62 336 338 348 350 390 392 396 398 438 440
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: 440
Found by: HenkM
db: batch=76, k=14, 58 274 10 40 4 40

STPT(10)	1022685802706828969	0 2 42 44 60 62 78 80 120 122	-1629023841162
SPT(16)	1022686054022222761	0 6 30 40 70 120 132 168 190 226 238 288 318 328 352 358	-1377708447370
TPT(14)	1022686325264513639	0 2 42 44 90 92 162 164 168 170 198 200 228 230	-1106466156492
SPT(16)	1022686918526337341	0 12 26 72 140 156 200 216 236 252 296 312 380 426 440 452	-513204332790
SPT(16)	1022687106855054947	0 12 26 54 62 96 144 152 174 182 230 264 272 300 314 326	-324875615184
SPT(16)	1022687417720043221	0 2 12 20 26 42 110 116 126 132 200 216 222 230 240 242	-14010626910
STPT(10)	1022687883194412437	0 2 30 32 60 62 90 92 120 122	451463742306
TPT(14)	1022688032310605357	0 2 54 56 144 146 222 224 264 266 270 272 294 296	600579935226
STPT(10)	1022688153030114377	0 2 42 44 72 74 102 104 144 146	721299444246
SPT(16)	1022688236990141077	0 4 24 42 52 70 82 100 126 144 156 174 184 202 222 226	805259470946
SPT(16)	1022688331761276847	0 6 16 42 66 90 102 132 154 184 196 220 244 270 280 286	900030606716