Prime p₀= 2431561471132599437 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 22 2 46 2 10 2 64 2 (?)
a_n: 0 2 30 32 60 62 84 86 132 134 144 146 210 212
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: 212
Found by: JonS
db: batch=82, k=14, 28 28 22 46 10 64

SPT(16)	2431560400729916777	0 54 60 66 96 102 116 126 170 180 194 200 230 236 242 296	-1070402682660
SPT(16)	2431560599526268291	0 12 60 72 90 118 132 138 202 208 222 250 268 280 328 340	-871606331146
STPT(10)	2431560871912520531	0 2 78 80 138 140 198 200 276 278	-599220078906
STPT(10)	2431560932805766121	0 2 6 8 48 50 90 92 96 98	-538326833316
STPT(12)	2431560993983668289	0 2 12 14 30 32 120 122 138 140 150 152	-477148931148
SPT(16)	2431561295889359407	0 34 36 54 64 112 120 142 144 166 174 222 232 250 252 286	-175243240030
SPT(16)	2431561574463739021	0 42 100 126 166 208 232 276 292 336 360 402 442 468 526 568	103331139584
SPT(16)	2431561905631753457	0 120 150 170 210 234 246 290 300 344 356 380 420 440 470 590	434499154020
TPT(14)	2431562662099404917	0 2 24 26 54 56 72 74 354 356 402 404 462 464	1190966805480
STPT(10)	2431563180278429339	0 2 18 20 30 32 42 44 60 62	1709145829902
SPT(16)	2431563323323098169	0 18 30 60 64 88 102 142 240 280 294 318 322 352 364 382	1852190498732