Prime p₀= 2972588448366058757 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 52 2 76 2 76 2 52 2 (?)
a_n: 0 2 54 56 132 134 210 212 264 266
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: 266
Found by: Orange Kid
db: batch=82, k=10, 2 52 2 76 2

SPT(16)	2972587306113742783	0 34 78 126 138 144 148 160 174 186 190 196 208 256 300 334	-1142252315974
SPT(16)	2972587390984148939	0 60 72 84 110 152 170 222 242 294 312 354 380 392 404 464	-1057381909818
SPT(13)	2972587469834540489	0 42 54 72 114 144 162 180 210 252 270 282 324	-978531518268
STPT(10)	2972587575938210939	0 2 18 20 60 62 102 104 120 122	-872427847818
SPT(16)	2972587717722076067	0 12 54 74 104 122 126 180 236 290 294 312 342 362 404 416	-730643982690
SPT(16)	2972588388284249027	0 102 146 170 186 230 242 252 254 264 276 320 336 360 404 506	-60081809730
STPT(10)	2972588592229529639	0 2 42 44 60 62 78 80 120 122	143863470882
SPT(16)	2972588711622718417	0 54 64 102 160 190 210 216 250 256 276 306 364 402 412 466	263256659660
TPT(14)	2972589110839853507	0 2 72 74 90 92 120 122 132 134 144 146 210 212	662473794750
SPT(16)	2972589338519560343	0 8 20 26 38 138 150 188 408 446 458 558 570 576 588 596	890153501586
STPT(10)	2972589775557581747	0 2 12 14 42 44 72 74 84 86	1327191522990