Prime p₀= 2328708417751985987 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 4 2 10 2 148 2 130 2 34 2 (?)
a_n: 0 2 84 86 90 92 102 104 252 254 384 386 420 422
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: 422
Found by: Landjunge
db: batch=81, k=14, 82 4 10 148 130 34

SPT(16)	2328707565623462593	0 36 84 100 166 180 190 226 258 294 304 318 384 400 448 484	-852128523394
STPT(10)	2328707625142662521	0 2 6 8 18 20 30 32 36 38	-792609323466
SPT(16)	2328708170341360399	0 54 72 130 160 168 228 238 384 394 454 462 492 550 568 622	-247410625588
SPT(16)	2328708179176837669	0 4 28 70 82 94 112 138 154 180 198 210 222 264 288 292	-238575148318
STPT(10)	2328708225132656357	0 2 12 14 42 44 72 74 84 86	-192619329630
SPT(16)	2328708267945947599	0 12 54 82 90 112 130 144 148 162 180 202 210 238 280 292	-149806038388
SPT(16)	2328708681856912123	0 4 10 28 30 60 70 108 136 174 184 214 216 234 240 244	264104926136
SPT(16)	2328708685171818253	0 30 94 100 118 178 184 234 250 300 306 366 384 390 454 484	267419832266
SPT(16)	2328708739033477349	0 14 30 38 104 108 128 134 168 174 194 198 264 272 288 302	321281491362
STPT(10)	2328708796561231727	0 2 30 32 42 44 54 56 84 86	378809245740
STPT(10)	2328709109317447457	0 2 42 44 72 74 102 104 144 146	691565461470