Prime p₀= 2124580997666597441 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 64 2 70 2 100 2 34 2 52 2 (?)
a_n: 0 2 30 32 96 98 168 170 270 272 306 308 360 362
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: 362
Found by: Time_Traveler
db: batch=80, k=14, 28 64 70 100 34 52

SPT(16)	2124579307510234933	0 18 30 78 100 114 124 130 138 144 154 168 190 238 250 268	-1690156362508
TPT(14)	2124579546976238249	0 2 18 20 42 44 60 62 72 74 78 80 228 230	-1450690359192
SPT(16)	2124579873734885383	0 6 40 70 84 90 166 180 190 204 280 286 300 330 364 370	-1123931712058
SPT(16)	2124579941962156387	0 22 52 60 112 126 132 144 262 274 280 294 346 354 384 406	-1055704441054
SPT(16)	2124579970599644269	0 10 34 40 88 130 154 160 222 228 252 294 342 348 372 382	-1027066953172
SPT(16)	2124580933131410213	0 38 108 120 146 150 168 176 180 188 206 210 236 248 318 356	-64535187228
SPT(16)	2124581367587382637	0 16 22 66 112 126 136 156 160 180 190 204 250 294 300 316	369920785196
STPT(10)	2124581370236575037	0 2 60 62 72 74 84 86 144 146	372569977596
SPT(16)	2124581744195378471	0 2 42 80 90 126 198 210 278 290 362 398 408 446 486 488	746528781030
STPT(10)	2124582366862034237	0 2 30 32 72 74 114 116 144 146	1369195436796
SPT(18)	2124582503180680069	0 24 42 52 90 94 150 174 252 280 358 382 438 442 480 490 508 532	1505514082628