Prime p₀= 235577728009600391 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 58 2 64 2 28 2 28 2 28 2 (?)
a_n: 0 2 60 62 126 128 156 158 186 188 216 218
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: 218
Found by: Megacruncher
db: batch=69, k=12, 58 64 28 28 28

SPT(14)	235577621554670561	0 6 8 20 48 78 80 108 110 140 168 180 182 188	-106454929830
SPT(16)	235577642767337011	0 16 52 60 70 102 108 130 168 190 196 228 238 246 282 298	-85242263380
SPT(14)	235577651950713851	0 8 30 48 78 108 120 218 230 260 290 308 330 338	-76058886540
SPT(14)	235577705702092753	0 4 16 18 30 58 60 94 96 124 136 138 150 154	-22307507638
SPT(14)	235577710203123679	0 28 40 42 54 58 70 102 114 118 130 132 144 172	-17806476712
SPT(14)	235577715242073121	0 58 60 66 108 156 198 208 250 298 340 346 348 406	-12767527270
TPT(12)	235577747913934241	0 2 6 8 60 62 96 98 138 140 228 230	19904333850
SPT(14)	235577796442062079	0 10 12 52 54 88 108 124 144 178 180 220 222 232	68432461688
SPT(14)	235577799538344143	0 38 48 60 66 104 110 144 150 188 194 206 216 254	71528743752
TPT(12)	235577838824732627	0 2 84 86 144 146 150 152 210 212 240 242	110815132236
TPT(14)	235577843504149847	0 2 30 32 72 74 84 86 114 116 150 152 162 164	115494549456