Prime p₀= 862720059999089597 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 22 2 4 2 22 2 28 2 (?)
a_n: 0 2 30 32 54 56 60 62 84 86 114 116
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: 116
Found by: [SG-2W]Kurzer
db: batch=73, k=12, 2 28 2 22 2 4

SPT(16)	862718735440840247	0 50 72 84 90 92 102 120 194 212 222 224 230 242 264 314	-1324558249350
TPT(14)	862718971489603637	0 2 90 92 120 122 162 164 192 194 204 206 222 224	-1088509485960
SPT(16)	862719373870415261	0 12 56 78 128 156 158 168 170 180 182 210 260 282 326 338	-686128674336
STPT(10)	862719649257217247	0 2 60 62 72 74 84 86 144 146	-410741872350
STPT(10)	862719776704413317	0 2 30 32 42 44 54 56 84 86	-283294676280
SPT(16)	862720059999089573	0 8 24 26 54 56 78 80 84 86 108 110 138 140 156 164	-24
TPT(14)	862720154133739409	0 2 30 32 60 62 102 104 138 140 198 200 228 230	94134649812
SPT(16)	862720305326139131	0 2 18 36 56 60 62 86 102 126 128 132 152 170 186 188	245327049534
SPT(16)	862720443519277171	0 6 12 22 48 52 58 66 82 90 96 100 126 136 142 148	383520187574
SPT(16)	862720578501481943	0 26 38 60 68 74 84 140 144 200 210 216 224 246 258 284	518502392346
STPT(10)	862720681438758809	0 2 18 20 30 32 42 44 60 62	621439669212