Prime p₀= 335915191848021827 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 40 2 178 2 10 2 4 2 (?)
a_n: 0 2 30 32 72 74 252 254 264 266 270 272
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: 272
Found by: Cruncher Pete
db: batch=70, k=12, 28 40 178 10 4

SPT(14)	335915153643906227	0 2 30 32 74 132 140 174 182 240 282 284 312 314	-38204115600
SPT(14)	335915159058924317	0 12 42 92 132 146 164 192 210 224 264 314 344 356	-32789097510
SPT(20)	335915165535866509	0 28 40 90 108 112 192 238 292 300 340 348 402 448 528 532 550 600 612 640	-26312155318
SPT(14)	335915168822232847	0 22 24 40 42 52 60 64 72 82 84 100 102 124	-23025788980
TPT(12)	335915169688134269	0 2 60 62 72 74 120 122 198 200 288 290	-22159887558
SPT(14)	335915190219006667	0 66 114 142 154 166 180 196 210 222 234 262 310 376	-1629015160
SPT(14)	335915199298948793	0 14 20 24 38 60 80 108 128 150 164 168 174 188	7450926966
SPT(14)	335915205318493019	0 14 24 128 140 168 170 198 200 228 240 344 354 368	13470471192
TPT(12)	335915215274178467	0 2 12 14 30 32 42 44 102 104 144 146	23426156640
STPT(10)	335915226532554167	0 2 30 32 72 74 114 116 144 146	34684532340
SPT(14)	335915248665819553	0 70 100 106 148 168 174 190 196 216 258 264 294 364	56817797726