Prime p₀= 1437081142444787897 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 16 2 88 2 58 2 22 2 58 2 (?)
a_n: 0 2 12 14 30 32 120 122 180 182 204 206 264 266
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: 266
Found by: Theadalus
db: batch=78, k=14, 10 16 88 58 22 58

SPT(16)	1437079507202888431	0 10 12 18 42 46 60 70 78 88 102 106 130 136 138 148	-1635241899466
SPT(20)	1437079960705774061	0 26 42 78 96 120 152 206 222 290 348 416 432 486 518 542 560 596 612 638	-1181739013836
SPT(16)	1437079985259688421	0 2 56 92 98 168 170 186 302 318 320 390 396 432 486 488	-1157185099476
STPT(10)	1437080278219088681	0 2 6 8 48 50 90 92 96 98	-864225699216
STPT(10)	1437080682171347999	0 2 30 32 60 62 90 92 120 122	-460273439898
SPT(16)	1437081042375551077	0 30 36 66 84 102 114 126 130 142 154 172 190 220 226 256	-100069236820
SPT(16)	1437081684017788849	0 28 138 148 178 234 270 300 418 448 484 540 570 580 690 718	541573000952
SPT(16)	1437082495473936673	0 6 46 76 96 160 220 228 238 246 306 370 390 420 460 466	1353029148776
SPT(16)	1437082550940839119	0 22 28 58 64 70 78 84 88 94 102 108 114 144 150 172	1408496051222
SPT(16)	1437082780626433033	0 34 64 70 90 156 186 214 216 244 274 340 360 366 396 430	1638181645136
TPT(14)	1437083054442127007	0 2 42 44 102 104 114 116 180 182 324 326 474 476	1911997339110