Prime p₀= 2509178352981056969 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 16 2 40 2 40 2 16 2 (?)
a_n: 0 2 18 20 60 62 102 104 120 122
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: 122
Found by: Hightower
db: batch=82, k=10, 2 16 2 40 2

SPT(16)	2509176470765527333	0 36 40 78 108 130 148 154 390 396 414 436 466 504 508 544	-1882215529636
STPT(10)	2509176642117413249	0 2 42 44 60 62 78 80 120 122	-1710863643720
SPT(16)	2509177175879136227	0 2 50 90 122 126 170 192 194 216 260 264 296 336 384 386	-1177101920742
TPT(14)	2509177880832663449	0 2 78 80 120 122 132 134 138 140 168 170 288 290	-472148393520
SPT(16)	2509178136569604667	0 24 52 94 102 112 154 214 222 282 324 334 342 384 412 436	-216411452302
SPT(16)	2509178183647951843	0 10 16 46 118 126 136 208 228 300 310 318 390 420 426 436	-169333105126
STPT(10)	2509178367154621397	0 2 42 44 72 74 102 104 144 146	14173564428
SPT(16)	2509178518879672867	0 12 16 40 52 100 190 192 250 252 342 390 402 426 430 442	165898615898
SPT(16)	2509178864302017827	0 24 56 62 86 90 104 126 170 192 206 210 234 240 272 296	511320960858
STPT(12)	2509179083653113041	0 2 30 32 60 62 126 128 156 158 186 188	730672056072
SPT(16)	2509180435906238863	0 88 108 114 124 138 156 178 216 238 256 270 280 286 306 394	2082925181894