Prime p₀= 2417427366724308767 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 136 2 10 2 28 2 4 2 40 2 (?)
a_n: 0 2 24 26 162 164 174 176 204 206 210 212 252 254
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: 254
Found by: [SG-FC] hl
db: batch=82, k=14, 22 136 10 28 4 40

SPT(16)	2417425146632013853	0 4 60 100 154 184 256 268 306 318 390 420 474 514 570 574	-2220092294914
STPT(10)	2417425462999873967	0 2 42 44 132 134 222 224 264 266	-1903724434800
STPT(10)	2417425663204287521	0 2 36 38 78 80 120 122 156 158	-1703520021246
SPT(16)	2417426436040736909	0 38 54 90 122 164 182 224 228 270 288 330 362 398 414 452	-930683571858
STPT(10)	2417426473210690157	0 2 60 62 72 74 84 86 144 146	-893513618610
STPT(10)	2417426862131503049	0 2 18 20 60 62 102 104 120 122	-504592805718
SPT(16)	2417427557523335849	0 20 44 74 78 98 104 128 174 198 204 224 228 258 282 302	190799027082
SPT(16)	2417427938883694577	0 2 32 42 102 140 162 222 284 344 366 404 464 474 504 506	572159385810
SPT(16)	2417428221141782777	0 60 66 96 144 146 180 236 300 356 390 392 440 470 476 536	854417474010
STPT(10)	2417428373511783857	0 2 30 32 42 44 54 56 84 86	1006787475090
SPT(16)	2417428391910187769	0 14 24 50 68 92 98 138 164 204 210 234 252 278 288 302	1025185879002