Prime p₀= 2338703274364400681 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 70 2 16 2 10 2 64 2 10 2 (?)
a_n: 0 2 78 80 150 152 168 170 180 182 246 248 258 260
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: 260
Found by: Landjunge
db: batch=81, k=14, 76 70 16 10 64 10

SPT(16)	2338702433910581411	0 8 18 56 72 116 128 156 182 210 222 266 282 320 330 338	-840453819270
SPT(16)	2338702562095939057	0 16 22 30 46 196 204 214 222 232 240 390 406 414 420 436	-712268461624
SPT(18)	2338702609711946909	0 44 120 140 162 168 200 270 288 434 452 522 554 560 582 602 678 722	-664652453772
SPT(16)	2338702625275784857	0 124 136 166 214 222 294 312 364 382 454 462 510 540 552 676	-649088615824
SPT(16)	2338702696220897821	0 42 52 90 148 178 190 220 258 288 300 330 388 426 436 478	-578143502860
TPT(14)	2338702841738100821	0 2 96 98 240 242 390 392 396 398 450 452 516 518	-432626299860
STPT(10)	2338703444414066699	0 2 12 14 30 32 48 50 60 62	170049666018
STPT(10)	2338703483157349937	0 2 30 32 72 74 114 116 144 146	208792949256
STPT(10)	2338704663004343729	0 2 18 20 30 32 42 44 60 62	1388639943048
SPT(16)	2338704694683689599	0 24 70 82 94 100 114 150 154 190 204 210 222 234 280 304	1420319288918
SPT(16)	2338704735794647469	0 62 140 174 210 230 242 252 272 282 294 314 350 384 462 524	1461430246788