Prime p₀= 2544145494002358977 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 28 2 166 2 10 2 34 2 28 2 (?)
a_n: 0 2 54 56 84 86 252 254 264 266 300 302 330 332
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: 332
Found by: Penguin
db: batch=82, k=14, 52 28 166 10 34 28

SPT(16)	2544143913029664713	0 36 60 66 78 80 98 104 120 126 144 146 158 164 188 224	-1580972694264
STPT(10)	2544144279635361839	0 2 42 44 60 62 78 80 120 122	-1214366997138
SPT(16)	2544144343350780661	0 30 78 82 100 102 112 192 226 306 316 318 336 340 388 418	-1150651578316
STPT(10)	2544144474257650007	0 2 30 32 102 104 174 176 204 206	-1019744708970
TPT(14)	2544144515030009501	0 2 30 32 78 80 150 152 240 242 390 392 420 422	-978972349476
STPT(12)	2544145483005982127	0 2 30 32 42 44 72 74 84 86 114 116	-10996376850
STPT(10)	2544145517345729021	0 2 6 8 48 50 90 92 96 98	23343370044
STPT(10)	2544145814997600641	0 2 36 38 78 80 120 122 156 158	320995241664
SPT(16)	2544145860932024467	0 40 132 156 172 174 184 196 240 252 262 264 280 304 396 436	366929665490
SPT(16)	2544146632280729977	0 12 34 70 106 120 132 144 232 244 256 270 306 342 364 376	1138278371000
SPT(16)	2544146649682031981	0 42 72 80 116 122 126 140 168 182 186 192 228 236 266 308	1155679673004