Prime p₀= 2565124223391956357 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 24 56 24 28 2 16 32 70 32 16 2 28 24 56 24 (?)
a_n: 0 24 80 104 132 134 150 182 252 284 300 302 330 354 410 434
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: 434
Found by: JayPi
db: batch=82, k=16, 24 56 24 28 2 16 32 70

SPT(16)	2565122847335972377	0 4 84 102 112 160 220 264 292 336 396 444 454 472 552 556	-1376055983980
STPT(10)	2565123168029189627	0 2 30 32 72 74 114 116 144 146	-1055362766730
STPT(10)	2565123450329567717	0 2 42 44 72 74 102 104 144 146	-773062388640
STPT(10)	2565123531667585697	0 2 54 56 72 74 90 92 144 146	-691724370660
TPT(14)	2565123785766759209	0 2 198 200 222 224 312 314 390 392 408 410 432 434	-437625197148
SPT(16)	2565124066946519293	0 10 34 88 94 144 174 270 304 400 430 480 486 540 564 574	-156445437064
STPT(10)	2565124532156913227	0 2 54 56 72 74 90 92 144 146	308764956870
SPT(16)	2565124851109739747	0 2 14 36 54 72 80 86 90 96 104 122 140 162 174 176	627717783390
STPT(10)	2565124882106456627	0 2 12 14 42 44 72 74 84 86	658714500270
SPT(16)	2565125369411025451	0 16 72 78 90 106 118 120 238 240 252 268 280 286 342 358	1146019069094
SPT(16)	2565125400639429193	0 10 24 40 114 144 154 178 186 210 220 250 324 340 354 364	1177247472836