Prime p₀= 1971727521412359197 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 40 2 4 2 40 2 10 2 (?)
a_n: 0 2 12 14 54 56 60 62 102 104 114 116
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: Cruncher Pete
db: batch=80, k=12, 2 10 2 40 2 4

SPT(16)	1971726099377732353	0 6 24 36 40 66 90 106 138 154 178 204 208 220 238 244	-1422034626844
STPT(10)	1971726298184463641	0 2 6 8 18 20 30 32 36 38	-1223227895556
SPT(16)	1971726664676628779	0 2 24 90 104 134 150 164 300 314 330 360 374 440 462 464	-856735730418
SPT(16)	1971727166612785807	0 16 30 40 52 70 106 162 184 240 276 294 306 316 330 346	-354799573390
STPT(10)	1971727223044335257	0 2 54 56 72 74 90 92 144 146	-298368023940
SPT(16)	1971727240497795863	0 18 20 26 78 84 90 98 186 194 200 206 258 264 266 284	-280914563334
STPT(10)	1971727875385595609	0 2 42 44 60 62 78 80 120 122	353973236412
SPT(16)	1971727898222229817	0 40 54 106 112 132 154 186 190 222 244 264 270 322 336 376	376809870620
STPT(10)	1971728008674653027	0 2 30 32 42 44 54 56 84 86	487262293830
SPT(16)	1971728117975794973	0 48 56 68 78 86 98 110 114 126 138 146 156 168 176 224	596563435776
STPT(10)	1971728257026632519	0 2 18 20 30 32 42 44 60 62	735614273322