Prime p₀= 1331272574883122021 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 58 2 82 2 4 2 40 2 40 2 (?)
a_n: 0 2 66 68 126 128 210 212 216 218 258 260 300 302
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 302
Found by: vaughan
db: batch=77, k=14, 64 58 82 4 40 40

SPT(16)	1331271669860402219	0 32 48 54 74 120 138 180 182 224 242 288 308 314 330 362	-905022719802
STPT(10)	1331271780186298997	0 2 54 56 72 74 90 92 144 146	-794696823024
SPT(16)	1331271828578929453	0 6 24 46 66 76 100 166 228 294 318 328 348 370 388 394	-746304192568
SPT(20)	1331272030209551449	0 28 40 84 94 160 174 244 264 312 370 418 438 508 522 588 598 642 654 682	-544673570572
SPT(16)	1331272234290071473	0 4 24 46 60 70 88 148 186 246 264 274 288 310 330 334	-340593050548
STPT(10)	1331272389427760951	0 2 78 80 108 110 138 140 216 218	-185455361070
SPT(16)	1331272605596712539	0 8 74 134 168 182 272 300 362 390 480 494 528 588 654 662	30713590518
TPT(14)	1331272892657995871	0 2 6 8 126 128 150 152 276 278 306 308 330 332	317774873850
SPT(16)	1331272946873394913	0 34 136 150 208 220 226 334 420 528 534 546 604 618 720 754	371990272892
TPT(14)	1331273057057179361	0 2 240 242 270 272 378 380 450 452 690 692 726 728	482174057340
SPT(16)	1331273068546934231	0 6 36 78 96 98 120 138 140 158 180 182 200 242 272 278	493663812210