Prime p₀= 1124762728799075369 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 4 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 48 50 78 80 90 92
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: 92
Found by: crashtech
db: batch=76, k=12, 2 10 2 28 2 4

SPT(16)	1124762176135564223	0 56 116 138 140 168 180 186 200 206 218 246 248 270 330 386	-552663511146
SPT(16)	1124762340848335169	0 44 60 110 128 158 168 170 192 194 204 234 252 302 318 362	-387950740200
STPT(10)	1124762443946770127	0 2 42 44 72 74 102 104 144 146	-284852305242
STPT(10)	1124762453639518427	0 2 30 32 42 44 54 56 84 86	-275159556942
SPT(16)	1124762596899369853	0 28 34 66 78 118 130 196 228 294 306 346 358 390 396 424	-131899705516
STPT(12)	1124762725586323037	0 2 12 14 42 44 60 62 90 92 102 104	-3212752332
SPT(16)	1124763189452959523	0 26 68 78 96 98 120 126 158 164 186 188 206 216 258 284	460653884154
SPT(16)	1124763695190151087	0 10 12 36 52 54 64 70 96 102 112 114 130 154 156 166	966391075718
SPT(16)	1124763875055352723	0 6 16 60 70 76 118 126 148 156 198 204 214 258 268 274	1146256277354
SPT(13)	1124764188424737691	0 12 18 42 132 150 180 210 228 318 342 348 360	1459625662322
SPT(16)	1124764672793488907	0 12 14 20 26 42 50 56 60 66 74 90 96 102 104 116	1943994413538