Prime p₀= 2037237015667184657 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 40 2 28 2 28 2 40 2 (?)
a_n: 0 2 42 44 72 74 102 104 144 146
All 10 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 146
Found by: Landjunge
db: batch=80, k=10, 2 40 2 28 2

SPT(16)	2037236254087885507	0 4 10 24 30 70 72 100 126 154 156 196 202 216 222 226	-761579299150
TPT(14)	2037236589370038029	0 2 42 44 78 80 120 122 150 152 198 200 252 254	-426297146628
SPT(16)	2037236677951932983	0 56 60 110 140 164 168 180 224 236 240 264 294 344 348 404	-337715251674
SPT(20)	2037236680348439981	0 26 32 36 60 66 78 92 138 158 210 230 276 290 302 308 332 336 342 368	-335318744676
SPT(16)	2037236849559535193	0 8 36 44 48 96 114 168 176 230 248 296 300 308 336 344	-166107649464
STPT(10)	2037236930346479177	0 2 30 32 42 44 54 56 84 86	-85320705480
SPT(16)	2037237148488009301	0 16 18 30 40 96 100 126 142 168 172 228 238 250 252 268	132820824644
STPT(10)	2037237161003213969	0 2 48 50 60 62 72 74 120 122	145336029312
SPT(16)	2037237229742526451	0 6 28 30 66 106 118 148 168 198 210 250 286 288 310 316	214075341794
SPT(16)	2037237382430398979	0 48 90 120 132 134 158 168 194 204 228 230 242 272 314 362	366763214322
TPT(14)	2037237893223100961	0 2 120 122 126 128 156 158 198 200 306 308 390 392	877555916304