Prime p₀= 1023123294260757223 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 4 26 18 36 16 20 10 14 10 20 16 36 18 26 4 (?)
a_n: 0 4 30 48 84 100 120 130 144 154 174 190 226 244 270 274
All 16 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 274
Found by: stoneageman
db: batch=76, k=16, 4 26 18 36 16 20 10 14

SPT(16)	1023122055924773443	0 6 28 48 66 126 130 144 160 174 178 238 256 276 298 304	-1238335983780
STPT(10)	1023122213795511461	0 2 30 32 78 80 126 128 156 158	-1080465245762
STPT(10)	1023122556018726341	0 2 6 8 48 50 90 92 96 98	-738242030882
SPT(16)	1023122702239528543	0 64 90 100 118 160 204 226 258 280 324 366 384 394 420 484	-592021228680
STPT(10)	1023123006961271927	0 2 12 14 42 44 72 74 84 86	-287299485296
SPT(16)	1023123100899679229	0 32 48 62 72 98 108 140 192 224 234 260 270 284 300 332	-193361077994
SPT(16)	1023123473530125833	0 20 24 48 56 78 98 108 206 216 236 258 266 290 294 314	179269368610
STPT(10)	1023123595771733549	0 2 30 32 60 62 90 92 120 122	301510976326
SPT(20)	1023123633019864141	0 6 10 30 58 72 82 126 132 178 240 286 292 336 346 360 388 408 412 418	338759106918
SPT(16)	1023124000331880977	0 6 36 132 230 236 246 252 314 320 330 336 434 530 560 566	706071123754
STPT(10)	1023124106130947867	0 2 54 56 72 74 90 92 144 146	811870190644