Prime p₀= 2739022143135484469 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 10 2 10 2 178 2 4 2 28 2 (?)
a_n: 0 2 18 20 30 32 42 44 222 224 228 230 258 260
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: 260
Found by: [SG-2W]Kurzer
db: batch=82, k=14, 16 10 10 178 4 28

SPT(16)	2739021311854268957	0 20 26 36 80 96 110 116 126 132 146 162 206 216 222 242	-831281215512
SPT(16)	2739021571985918291	0 30 42 72 102 156 158 200 228 270 272 326 356 386 398 428	-571149566178
STPT(10)	2739021604912364867	0 2 30 32 42 44 54 56 84 86	-538223119602
STPT(10)	2739021717022369661	0 2 36 38 78 80 120 122 156 158	-426113114808
SPT(16)	2739021734498309011	0 10 16 42 48 66 82 96 112 126 142 160 166 192 198 208	-408637175458
STPT(10)	2739021951559944899	0 2 30 32 60 62 90 92 120 122	-191575539570
SPT(16)	2739022264555994941	0 28 42 66 118 166 168 196 222 250 252 300 352 376 390 418	121420510472
SPT(16)	2739022281063015463	0 60 66 88 106 120 126 256 318 448 454 468 486 508 514 574	137927530994
TPT(14)	2739022431587609579	0 2 60 62 168 170 192 194 198 200 228 230 240 242	288452125110
SPT(16)	2739022502010294289	0 10 34 54 84 124 168 192 280 304 348 388 418 438 462 472	358874809820
SPT(16)	2739022530362263661	0 42 66 80 102 150 206 216 242 252 308 356 378 392 416 458	387226779192