Prime p₀= 1144183870221852767 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 220 2 10 2 34 2 10 2 220 2 (?)
a_n: 0 2 222 224 234 236 270 272 282 284 504 506
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: 506
Found by: Vitalii Koshura
db: batch=76, k=12, 2 220 2 10 2 34

SPT(16)	1144181792795729801	0 26 32 36 42 92 150 152 276 278 336 386 392 396 402 428	-2077426122966
STPT(10)	1144181895780766877	0 2 60 62 72 74 84 86 144 146	-1974441085890
SPT(16)	1144182018422330929	0 12 42 94 108 118 132 142 150 160 174 184 198 250 280 292	-1851799521838
TPT(14)	1144182370905159281	0 2 48 50 90 92 216 218 246 248 288 290 348 350	-1499316693486
STPT(10)	1144182886419961481	0 2 30 32 60 62 90 92 120 122	-983801891286
SPT(16)	1144183188813742381	0 10 90 96 108 118 132 150 178 196 210 220 232 238 318 328	-681408110386
STPT(10)	1144184093203729187	0 2 30 32 42 44 54 56 84 86	222981876420
SPT(18)	1144184547854290651	0 46 48 60 78 88 108 118 148 198 228 238 258 268 286 298 300 346	677632437884
TPT(14)	1144184740014897179	0 2 18 20 102 104 240 242 282 284 408 410 420 422	869793044412
SPT(16)	1144184814875446991	0 6 12 36 78 92 96 108 110 122 126 140 182 206 212 218	944653594224
STPT(10)	1144184906203939421	0 2 6 8 48 50 90 92 96 98	1035982086654