Prime p₀= 1023123006961271927 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 28 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 72 74 84 86
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: 86
Found by: stoneageman
db: batch=76, k=10, 2 10 2 28 2

SPT(16)	1023121885298684599	0 18 24 30 58 64 108 154 264 310 354 360 388 394 400 418	-1121662587328
STPT(10)	1023122051857514429	0 2 18 20 30 32 42 44 60 62	-955103757498
SPT(16)	1023122055924773443	0 6 28 48 66 126 130 144 160 174 178 238 256 276 298 304	-951036498484
STPT(10)	1023122213795511461	0 2 30 32 78 80 126 128 156 158	-793165760466
STPT(10)	1023122556018726341	0 2 6 8 48 50 90 92 96 98	-450942545586
SPT(16)	1023122702239528543	0 64 90 100 118 160 204 226 258 280 324 366 384 394 420 484	-304721743384
SPT(16)	1023123100899679229	0 32 48 62 72 98 108 140 192 224 234 260 270 284 300 332	93938407302
SPT(16)	1023123294260757223	0 4 30 48 84 100 120 130 144 154 174 190 226 244 270 274	287299485296
SPT(16)	1023123473530125833	0 20 24 48 56 78 98 108 206 216 236 258 266 290 294 314	466568853906
STPT(10)	1023123595771733549	0 2 30 32 60 62 90 92 120 122	588810461622
SPT(20)	1023123633019864141	0 6 10 30 58 72 82 126 132 178 240 286 292 336 346 360 388 408 412 418	626058592214