Prime p₀= 26836719515098151 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 64 2 28 2 28 2 28 2 40 2 (?)
a_n: 0 2 66 68 96 98 126 128 156 158 198 200
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: 200
Found by: Farscape
db: batch=65, k=12, 64 28 28 28 40

SPT(14)	26836680203033413	0 6 70 76 100 114 138 196 220 234 258 264 328 334	-39312064738
SPT(14)	26836680228190009	0 4 52 72 108 112 118 144 150 154 190 210 258 262	-39286908142
SPT(14)	26836684143049903	0 30 48 108 136 154 160 174 180 198 226 286 304 334	-35372048248
SPT(20)	26836696121156687	0 24 44 54 84 90 126 156 164 176 294 306 314 344 380 386 416 426 446 470	-23393941464
SPT(14)	26836700785146157	0 6 10 24 34 54 66 124 136 156 166 180 184 190	-18729951994
SPT(14)	26836704697099079	0 68 72 98 102 132 200 210 278 308 312 338 342 410	-14817999072
TPT(12)	26836740990342821	0 2 18 20 30 32 150 152 198 200 306 308	21475244670
SPT(14)	26836754859440363	0 18 36 56 60 78 90 134 146 164 168 188 206 224	35344342212
SPT(14)	26836755926559937	0 36 72 100 102 106 112 144 150 154 156 184 220 256	36411461786
SPT(14)	26836758500888579	0 8 24 42 48 62 104 138 180 194 200 218 234 242	38985790428
SPT(14)	26836782277162813	0 16 18 30 36 118 120 154 156 238 244 256 258 274	62762064662