Prime p₀= 960272383768784837 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 58 2 22 2 4 2 22 2 58 2 (?)
a_n: 0 2 60 62 84 86 90 92 114 116 174 176
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 176
Found by: Theadalus
db: batch=76, k=12, 2 58 2 22 2 4

SPT(16)	960271753325191039	0 10 22 84 120 174 178 192 220 234 238 292 328 390 402 412	-630443593798
SPT(16)	960272019888809909	0 8 14 42 50 120 128 152 210 234 242 312 320 348 354 362	-363879974928
SPT(16)	960272129060498171	0 60 98 120 156 180 222 242 246 266 308 332 368 390 428 488	-254708286666
STPT(10)	960272244673366277	0 2 42 44 72 74 102 104 144 146	-139095418560
STPT(10)	960272246002177697	0 2 30 32 42 44 54 56 84 86	-137766607140
SPT(16)	960272356379279113	0 4 10 48 106 126 154 174 190 210 238 258 316 354 360 364	-27389505724
TPT(14)	960272737138405151	0 2 30 32 60 62 66 68 156 158 168 170 366 368	353369620314
SPT(16)	960272937618546847	0 10 52 84 114 154 234 252 262 280 360 400 430 462 504 514	553849762010
SPT(16)	960273198500519359	0 10 24 30 112 124 172 214 288 330 378 390 472 478 492 502	814731734522
SPT(16)	960273510861790271	0 6 20 48 110 116 170 198 308 336 390 396 458 486 500 506	1127093005434
STPT(10)	960273517352402129	0 2 30 32 60 62 90 92 120 122	1133583617292