Prime p₀= 2592627748607503181 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 40 2 10 2 4 2 82 2 76 2 (?)
a_n: 0 2 66 68 108 110 120 122 126 128 210 212 288 290
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: 290
Found by: JayPi
db: batch=82, k=14, 64 40 10 4 82 76

SPT(16)	2592625706765923729	0 18 54 124 162 174 208 228 274 294 328 340 378 448 484 502	-2041841579452
TPT(14)	2592625910969562227	0 2 84 86 90 92 132 134 180 182 222 224 270 272	-1837637940954
SPT(16)	2592626241091158227	0 26 36 90 96 120 216 222 224 230 326 350 356 410 420 446	-1507516344954
SPT(16)	2592626760163938569	0 12 54 80 102 120 122 128 234 240 242 260 282 308 350 362	-988443564612
SPT(16)	2592626939056356857	0 2 14 36 42 110 114 120 146 152 156 224 230 252 264 266	-809551146324
SPT(16)	2592627284055946777	0 6 12 72 76 90 112 150 226 264 286 300 304 364 370 376	-464551556404
SPT(16)	2592628014307058669	0 44 62 78 90 104 132 134 258 260 288 302 314 330 348 392	265699555488
STPT(10)	2592628014816756737	0 2 60 62 72 74 84 86 144 146	266209253556
SPT(16)	2592628562649856811	0 2 20 66 68 86 92 98 120 126 132 150 152 198 216 218	814042353630
STPT(10)	2592629199228269021	0 2 6 8 18 20 30 32 36 38	1450620765840
SPT(16)	2592629217992900323	0 6 84 90 100 184 196 210 250 264 276 360 370 376 454 460	1469385397142