Prime p₀= 1273809734161285967 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 40 2 28 2 16 2 28 2 40 2 (?)
a_n: 0 2 42 44 72 74 90 92 120 122 162 164
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: 164
Found by: HenkM
db: batch=77, k=12, 2 40 2 28 2 16

SPT(16)	1273808836139185391	0 26 38 50 62 78 86 90 128 132 140 156 168 180 192 218	-898022100576
STPT(10)	1273809151358418971	0 2 6 8 18 20 30 32 36 38	-582802866996
SPT(16)	1273809206919146393	0 14 60 84 96 104 114 116 138 140 150 158 170 194 240 254	-527242139574
STPT(10)	1273809400494832247	0 2 54 56 72 74 90 92 144 146	-333666453720
SPT(16)	1273809556017850589	0 2 8 72 78 80 108 110 180 182 210 212 218 282 288 290	-178143435378
SPT(16)	1273809577959047807	0 66 74 80 96 122 140 144 152 156 174 200 216 222 230 296	-156202238160
STPT(10)	1273810003409528327	0 2 12 14 42 44 72 74 84 86	269248242360
SPT(16)	1273810153858279381	0 58 100 130 142 156 186 210 268 292 322 336 348 378 420 478	419696993414
STPT(10)	1273810319886494417	0 2 24 26 42 44 60 62 84 86	585725208450
TPT(14)	1273810372096285979	0 2 42 44 72 74 138 140 198 200 222 224 258 260	637935000012
STPT(10)	1273810932338838329	0 2 42 44 60 62 78 80 120 122	1198177552362