Prime p₀= 278632921692706121 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 46 2 10 2 16 2 88 2 16 2 (?)
a_n: 0 2 48 50 60 62 78 80 168 170 186 188
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: 188
Found by: Ralfy
db: batch=69, k=12, 46 10 16 88 16

TPT(12)	278632783455956129	0 2 12 14 30 32 48 50 198 200 210 212	-138236749992
STPT(10)	278632800290770697	0 2 72 74 102 104 132 134 204 206	-121401935424
SPT(14)	278632835634811439	0 14 38 80 84 92 144 248 300 308 312 354 378 392	-86057894682
SPT(14)	278632861703507891	0 20 32 38 42 60 68 180 188 206 210 216 228 248	-59989198230
SPT(14)	278632887136392181	0 22 40 72 78 100 108 142 150 172 178 210 228 250	-34556313940
SPT(14)	278632900678896349	0 18 22 40 84 88 102 130 144 148 192 210 214 232	-21013809772
SPT(14)	278632947851552797	0 24 42 46 52 100 136 270 306 354 360 364 382 406	26158846676
SPT(14)	278632957338310621	0 12 16 30 36 76 90 112 126 166 172 186 190 202	35645604500
TPT(12)	278632960139703641	0 2 36 38 66 68 90 92 96 98 108 110	38446997520
SPT(16)	278632994933086081	0 10 12 18 46 82 88 112 126 150 156 192 220 226 228 238	73240379960
TPT(12)	278632998619484099	0 2 48 50 120 122 132 134 162 164 180 182	76926777978