Prime p₀= 4504040500925445869 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 100 2 4 2 58 2 10 2 58 2 (?)
a_n: 0 2 30 32 132 134 138 140 198 200 210 212 270 272
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: 272
Found by: Antares2022
db: batch=85, k=14, 28 100 4 58 10 58

SPT(16)	4504038111493537741	0 76 82 108 112 132 178 186 202 210 256 276 280 306 312 388	-2389431908128
SPT(13)	4504038216166814609	0 12 60 72 78 102 120 138 162 168 180 228 240	-2284758631260
TPT(14)	4504039814768371949	0 2 12 14 108 110 120 122 168 170 222 224 240 242	-686157073920
SPT(16)	4504040059759383947	0 12 86 96 156 212 216 282 350 416 420 476 536 546 620 632	-441166061922
STPT(10)	4504040391336548561	0 2 36 38 78 80 120 122 156 158	-109588897308
SPT(16)	4504040433370281719	0 42 48 60 102 104 144 188 234 278 318 320 362 374 380 422	-67555164150
SPT(16)	4504041751175436377	0 14 32 96 116 120 122 164 222 264 266 270 290 354 372 386	1250249990508
STPT(10)	4504041797772103127	0 2 30 32 72 74 114 116 144 146	1296846657258
STPT(10)	4504042011045227177	0 2 90 92 102 104 114 116 204 206	1510119781308
SPT(16)	4504042920753103031	0 6 30 38 56 62 80 108 230 258 276 282 300 308 332 338	2419827657162
SPT(16)	4504043265332709389	0 18 32 62 68 132 170 198 212 240 278 342 348 378 392 410	2764407263520