Prime p₀= 1282342616856020129 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 88 2 28 2 40 2 4 2 22 2 (?)
a_n: 0 2 90 92 180 182 210 212 252 254 258 260 282 284
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: 284
Found by: Theadalus
db: batch=77, k=14, 88 88 28 40 4 22

SPT(16)	1282342133565772319	0 18 24 50 74 80 84 140 162 218 222 228 252 278 284 302	-483290247810
SPT(13)	1282342190834745617	0 12 30 36 42 66 96 126 150 156 162 180 192	-426021274512
SPT(16)	1282342320705561377	0 12 20 62 86 92 126 174 212 260 294 300 324 366 374 386	-296150458752
SPT(16)	1282342328010183547	0 4 30 34 106 130 142 144 172 174 186 210 282 286 312 316	-288845836582
SPT(16)	1282342363654154839	0 18 84 142 168 192 262 274 318 330 400 424 450 508 574 592	-253201865290
SPT(16)	1282342540013188211	0 48 96 108 122 126 152 158 210 216 242 246 260 272 320 368	-76842831918
STPT(10)	1282343134954603607	0 2 30 32 42 44 54 56 84 86	518098583478
STPT(12)	1282343241623085977	0 2 24 26 30 32 54 56 60 62 84 86	624767065848
STPT(10)	1282343350561525331	0 2 30 32 78 80 126 128 156 158	733705505202
STPT(10)	1282343957337346637	0 2 24 26 42 44 60 62 84 86	1340481326508
SPT(16)	1282344143534048137	0 4 36 54 70 112 156 162 334 340 384 426 442 460 492 496	1526678028008