Prime p₀= 3022376342321648231 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 130 2 70 2 214 2 118 2 10 2 (?)
a_n: 0 2 6 8 138 140 210 212 426 428 546 548 558 560
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: 560
Found by: JayPi
db: batch=82, k=14, 4 130 70 214 118 10

SPT(16)	3022374878858559473	0 8 14 20 36 86 104 140 174 210 228 278 294 300 306 314	-1463463088758
STPT(10)	3022374902995902071	0 2 36 38 78 80 120 122 156 158	-1439325746160
SPT(16)	3022375084176981089	0 8 18 42 60 72 84 104 168 188 200 212 230 254 264 272	-1258144667142
SPT(18)	3022375112169134671	0 52 60 66 76 82 102 126 178 210 262 286 306 312 322 328 336 388	-1230152513560
STPT(10)	3022375163852579537	0 2 30 32 60 62 90 92 120 122	-1178469068694
SPT(16)	3022375344221368013	0 6 14 20 120 126 216 230 300 314 404 410 510 516 524 530	-998100280218
STPT(10)	3022376401776922439	0 2 18 20 30 32 42 44 60 62	59455274208
SPT(16)	3022377032356647463	0 18 28 66 88 106 180 186 190 196 270 288 310 348 358 376	690034999232
SPT(16)	3022377064604801341	0 22 58 60 70 96 100 120 208 228 232 258 268 270 306 328	722283153110
SPT(16)	3022377109599126997	0 16 42 46 112 126 132 186 310 364 370 384 450 454 480 496	767277478766
SPT(16)	3022377138900680699	0 68 108 140 144 158 168 180 248 260 270 284 288 320 360 428	796579032468