Prime p₀= 2838490483436971637 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 28 2 10 2 64 2 28 2 82 2 (?)
a_n: 0 2 42 44 72 74 84 86 150 152 180 182 264 266
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: 266
Found by: Roadranner
db: batch=82, k=14, 40 28 10 64 28 82

SPT(16)	2838489478239181199	0 2 24 38 60 72 104 144 278 318 350 362 384 398 420 422	-1005197790438
STPT(10)	2838489508756650779	0 2 18 20 30 32 42 44 60 62	-974680320858
SPT(16)	2838489671605272389	0 50 78 80 84 92 102 150 242 290 300 308 312 314 342 392	-811831699248
SPT(16)	2838489752768665991	0 2 102 156 198 212 218 266 312 360 366 380 422 476 576 578	-730668305646
SPT(16)	2838489771654817193	0 20 56 86 114 116 140 144 170 174 198 200 228 258 294 314	-711782154444
SPT(16)	2838490322243279177	0 6 80 90 104 110 126 134 192 200 216 222 236 246 320 326	-161193692460
STPT(10)	2838490572842428277	0 2 12 14 72 74 132 134 144 146	89405456640
STPT(10)	2838490736506919279	0 2 30 32 60 62 90 92 120 122	253069947642
SPT(16)	2838490837720081967	0 54 56 80 96 122 152 192 194 234 264 290 306 330 332 386	354283110330
TPT(14)	2838491253860297639	0 2 30 32 48 50 132 134 198 200 240 242 258 260	770423326002
STPT(10)	2838491537108047277	0 2 30 32 72 74 114 116 144 146	1053671075640