Prime p₀= 1596322072750565087 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 10 2 58 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 102 104 114 116 144 146
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: 146
Found by: [SG-2W]Kurzer
db: batch=78, k=12, 2 28 2 10 2 58

TPT(14)	1596320856715892369	0 2 12 14 18 20 150 152 240 242 270 272 402 404	-1216034672718
SPT(16)	1596320941352801819	0 24 38 42 68 74 108 150 152 194 228 234 260 264 278 302	-1131397763268
SPT(16)	1596321578341482631	0 16 28 42 46 52 66 72 106 112 126 132 136 150 162 178	-494409082456
SPT(16)	1596321688517122423	0 28 84 138 154 198 208 250 294 336 346 390 406 460 516 544	-384233442664
SPT(16)	1596321854050369847	0 42 90 92 114 122 150 174 200 224 252 260 282 284 332 374	-218700195240
STPT(10)	1596321880857758321	0 2 36 38 78 80 120 122 156 158	-191892806766
SPT(16)	1596322169023114993	0 84 204 208 238 250 270 358 360 448 468 480 510 514 634 718	96272549906
STPT(10)	1596322201496176541	0 2 30 32 78 80 126 128 156 158	128745611454
SPT(16)	1596322203242842973	0 6 8 30 60 66 80 98 108 126 140 146 176 198 200 206	130492277886
STPT(10)	1596322438171411859	0 2 18 20 30 32 42 44 60 62	365420846772
SPT(16)	1596322443695555057	0 42 54 66 80 84 86 170 276 360 362 366 380 392 404 446	370944989970