Prime p₀= 2797173820398400187 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 106 2 130 2 124 2 28 2 22 2 (?)
a_n: 0 2 24 26 132 134 264 266 390 392 420 422 444 446
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: 446
Found by: [SG-2W]Kurzer
db: batch=82, k=14, 22 106 130 124 28 22

TPT(14)	2797171853628890819	0 2 12 14 30 32 42 44 72 74 180 182 228 230	-1966769509368
STPT(12)	2797172022174283781	0 2 30 32 60 62 66 68 96 98 126 128	-1798224116406
SPT(16)	2797172037955136657	0 2 26 50 60 74 84 102 194 212 222 236 246 270 294 296	-1782443263530
TPT(14)	2797172626846236209	0 2 180 182 258 260 348 350 390 392 432 434 468 470	-1193552163978
TPT(14)	2797172715472658231	0 2 60 62 78 80 120 122 168 170 216 218 228 230	-1104925741956
STPT(10)	2797172959333653911	0 2 6 8 48 50 90 92 96 98	-861064746276
SPT(16)	2797174031428610531	0 18 32 60 102 152 200 228 230 258 306 356 398 426 440 458	211030210344
STPT(10)	2797174301510245817	0 2 30 32 42 44 54 56 84 86	481111845630
SPT(16)	2797174589760667661	0 20 42 62 86 96 138 156 182 200 242 252 276 296 318 338	769362267474
SPT(16)	2797174616134148161	0 6 10 18 22 60 70 88 90 108 118 156 160 168 172 178	795735747974
SPT(16)	2797174768854754579	0 54 78 102 154 222 228 264 298 334 340 408 460 484 508 562	948456354392