Prime p₀= 2124454282790013761 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 154 2 40 2 136 2 10 2 16 2 (?)
a_n: 0 2 30 32 186 188 228 230 366 368 378 380 396 398
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: 398
Found by: Landjunge
db: batch=80, k=14, 28 154 40 136 10 16

TPT(14)	2124453262763344967	0 2 24 26 42 44 84 86 150 152 210 212 240 242	-1020026668794
SPT(16)	2124453566169716101	0 22 48 66 78 106 132 162 166 196 222 250 262 280 306 328	-716620297660
SPT(16)	2124453611981180741	0 18 42 50 98 122 182 188 270 276 336 360 408 416 440 458	-670808833020
SPT(16)	2124453658776755753	0 6 20 30 56 74 84 90 194 200 210 228 254 264 278 284	-624013258008
SPT(16)	2124453909108509879	0 38 42 92 108 164 168 174 218 224 228 284 300 350 354 392	-373681503882
SPT(16)	2124454226653357789	0 28 42 198 208 238 280 292 390 402 444 474 484 640 654 682	-56136655972
STPT(10)	2124454389107967347	0 2 30 32 72 74 114 116 144 146	106317953586
SPT(16)	2124454406296208489	0 32 42 110 114 192 194 198 224 228 230 308 312 380 390 422	123506194728
STPT(10)	2124455005113278909	0 2 78 80 120 122 162 164 240 242	722323265148
STPT(10)	2124455132125844897	0 2 30 32 42 44 54 56 84 86	849335831136
SPT(16)	2124455337923807209	0 12 18 54 124 132 150 172 180 202 220 228 298 334 340 352	1055133793448