Prime p₀= 2678257914922615757 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 16 2 52 2 46 2 10 2 34 2 (?)
a_n: 0 2 12 14 30 32 84 86 132 134 144 146 180 182
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: 182
Found by: Asgard2022
db: batch=82, k=14, 10 16 52 46 10 34

SPT(16)	2678257080549906197	0 20 60 72 102 114 194 242 264 312 392 404 434 446 486 506	-834372709560
STPT(10)	2678257163820750947	0 2 30 32 42 44 54 56 84 86	-751101864810
SPT(16)	2678257186552745627	0 20 60 62 126 140 152 156 170 174 186 200 264 266 306 326	-728369870130
SPT(16)	2678257554717479281	0 22 42 88 108 148 150 166 192 208 210 250 270 316 336 358	-360205136476
SPT(16)	2678257581729040147	0 36 106 126 132 154 204 226 270 292 342 364 370 390 460 496	-333193575610
SPT(16)	2678257837085666851	0 42 52 100 108 168 178 190 360 372 382 442 450 498 508 550	-77836948906
SPT(16)	2678258144480342869	0 22 60 130 148 174 180 198 214 232 238 264 282 352 390 412	229557727112
SPT(16)	2678258183764129013	0 6 50 80 84 104 116 146 204 234 246 266 270 300 344 350	268841513256
SPT(16)	2678258251397251219	0 12 22 28 64 78 112 132 160 180 214 228 264 270 280 292	336474635462
STPT(10)	2678258459623045547	0 2 42 44 132 134 222 224 264 266	544700429790
SPT(16)	2678258637064804939	0 28 40 78 120 160 168 222 280 334 342 382 424 462 474 502	722142189182