Prime p₀= 216438093558276617 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 22 2 4 2 10 2 16 2 22 2 (?)
a_n: 0 2 24 26 30 32 42 44 60 62 84 86
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: 86
Found by: desktop64
db: batch=69, k=12, 22 4 10 16 22

SPT(16)	216438022664227961	0 6 56 78 86 108 168 192 266 290 350 372 380 402 452 458	-70894048656
SPT(14)	216438053847651091	0 30 46 70 82 102 106 162 166 186 198 222 238 268	-39710625526
SPT(16)	216438056725419103	0 28 66 94 124 126 138 148 186 196 208 210 240 268 306 334	-36832857514
TPT(12)	216438066251209487	0 2 60 62 84 86 102 104 180 182 282 284	-27307067130
SPT(14)	216438075721573259	0 8 38 42 50 54 72 80 98 102 110 114 144 152	-17836703358
SPT(14)	216438092725217633	0 18 78 90 134 144 174 230 260 270 314 326 386 404	-833058984
SPT(14)	216438097821337907	0 6 20 56 84 102 116 210 224 242 270 306 320 326	4263061290
TPT(12)	216438126652040477	0 2 30 32 42 44 72 74 120 122 132 134	33093763860
SPT(14)	216438128054436209	0 8 32 42 60 74 78 104 108 122 140 150 174 182	34496159592
STPT(10)	216438175548558881	0 2 30 32 78 80 126 128 156 158	81990282264
TPT(12)	216438202953936581	0 2 36 38 126 128 198 200 246 248 408 410	109395659964