Prime p₀= 2037236589370038029 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 34 2 40 2 28 2 46 2 52 2 (?)
a_n: 0 2 42 44 78 80 120 122 150 152 198 200 252 254
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: 254
Found by: Landjunge
db: batch=80, k=14, 40 34 40 28 46 52

SPT(16)	2037235792065419653	0 16 66 78 94 108 114 144 190 220 226 240 256 268 318 334	-797304618376
SPT(16)	2037235871264131007	0 2 30 84 92 110 122 134 270 282 294 312 320 374 402 404	-718105907022
SPT(16)	2037235878479501377	0 6 12 42 72 100 124 126 130 132 156 184 214 244 250 256	-710890536652
STPT(10)	2037236015558900381	0 2 36 38 78 80 120 122 156 158	-573811137648
STPT(10)	2037236085326226131	0 2 6 8 48 50 90 92 96 98	-504043811898
SPT(16)	2037236254087885507	0 4 10 24 30 70 72 100 126 154 156 196 202 216 222 226	-335282152522
SPT(16)	2037236677951932983	0 56 60 110 140 164 168 180 224 236 240 264 294 344 348 404	88581894954
SPT(20)	2037236680348439981	0 26 32 36 60 66 78 92 138 158 210 230 276 290 302 308 332 336 342 368	90978401952
SPT(16)	2037236849559535193	0 8 36 44 48 96 114 168 176 230 248 296 300 308 336 344	260189497164
STPT(10)	2037236930346479177	0 2 30 32 42 44 54 56 84 86	340976441148
STPT(10)	2037237015667184657	0 2 42 44 72 74 102 104 144 146	426297146628