Prime p₀= 239871951526856147 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 70 2 28 2 16 2 52 2 34 2 (?)
a_n: 0 2 72 74 102 104 120 122 174 176 210 212
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: 212
Found by: Megacruncher
db: batch=69, k=12, 70 28 16 52 34

SPT(14)	239871861839789351	0 6 12 56 72 86 90 152 156 170 186 230 236 242	-89687066796
SPT(14)	239871881059687553	0 6 14 20 24 66 68 96 98 140 144 150 158 164	-70467168594
SPT(14)	239871899781925727	0 114 122 150 170 180 194 240 254 264 284 312 320 434	-51744930420
SPT(14)	239871915392976367	0 22 30 34 36 90 96 190 196 250 252 256 264 286	-36133879780
SPT(14)	239871925857498877	0 10 24 34 40 54 60 244 250 264 270 280 294 304	-25669357270
SPT(14)	239871943273627543	0 6 54 60 76 88 90 154 156 168 184 190 238 244	-8253228604
SPT(16)	239871973714315099	0 24 28 58 70 72 112 124 138 150 190 192 204 234 238 262	22187458952
TPT(12)	239871984036045461	0 2 18 20 78 80 156 158 258 260 270 272	32509189314
SPT(14)	239872012720511671	0 10 78 90 142 148 180 220 252 258 310 322 390 400	61193655524
SPT(14)	239872023546151783	0 10 54 96 100 166 210 250 294 360 364 406 450 460	72019295636
SPT(14)	239872032740259757	0 4 40 54 82 84 120 154 190 192 220 234 270 274	81213403610