Prime p₀= 820141738154091137 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 10 2 4 2 10 2 10 2 (?)
a_n: 0 2 12 14 24 26 30 32 42 44 54 56
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: 56
Found by: Theadalus
db: batch=73, k=12, 2 10 2 10 2 4

SPT(16)	820141007441192477	0 20 24 32 62 80 84 96 110 122 126 144 174 182 186 206	-730712898660
TPT(16)	820141058572096277	0 2 30 32 84 86 120 122 144 146 162 164 300 302 354 356	-679581994860
STPT(10)	820141464894573707	0 2 54 56 72 74 90 92 144 146	-273259517430
STPT(10)	820141526570780501	0 2 6 8 48 50 90 92 96 98	-211583310636
SPT(16)	820141615077370763	0 8 20 84 86 108 114 150 224 260 266 288 290 354 366 374	-123076720374
TPT(14)	820141699807566599	0 2 78 80 108 110 180 182 192 194 222 224 240 242	-38346524538
SPT(16)	820141756423850009	0 2 14 24 48 84 90 92 120 122 128 164 188 198 210 212	18269758872
SPT(16)	820141800253045541	0 18 42 50 62 102 108 116 252 260 266 306 318 326 350 368	62098954404
STPT(10)	820141911614464247	0 2 12 14 72 74 132 134 144 146	173460373110
SPT(16)	820141994946727379	0 12 42 62 80 84 92 114 188 210 218 222 240 260 290 302	256792636242
SPT(16)	820142367888724781	0 6 26 66 68 98 102 116 132 146 150 180 182 222 242 248	629734633644