Prime p₀= 1245537789374663789 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 76 2 76 2 10 2 (?)
a_n: 0 2 12 14 90 92 168 170 180 182
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: 182
Found by: Megacruncher
db: batch=77, k=10, 2 10 2 76 2

SPT(16)	1245536822179144529	0 2 38 48 110 224 248 264 308 324 348 462 524 534 570 572	-967195519260
SPT(16)	1245536925759018701	0 2 20 50 72 78 90 92 96 98 110 116 138 168 186 188	-863615645088
SPT(16)	1245536959986376061	0 26 42 56 132 180 182 210 272 300 302 350 426 440 456 482	-829388287728
SPT(16)	1245537426679543273	0 96 100 106 136 138 204 250 264 310 376 378 408 414 418 514	-362695120516
SPT(16)	1245537518687702467	0 12 36 52 54 64 90 94 192 196 222 232 234 250 274 286	-270686961322
STPT(10)	1245537588812563127	0 2 12 14 72 74 132 134 144 146	-200562100662
STPT(10)	1245538252852574279	0 2 18 20 30 32 42 44 60 62	463477910490
STPT(10)	1245538561214708729	0 2 48 50 90 92 132 134 180 182	771840044940
SPT(16)	1245538587202852687	0 10 30 54 72 96 106 132 184 210 220 244 262 286 306 316	797828188898
TPT(14)	1245538902900716159	0 2 138 140 282 284 288 290 360 362 402 404 420 422	1113526052370
STPT(10)	1245539230824565067	0 2 30 32 42 44 54 56 84 86	1441449901278