Prime p₀= 2154830755004907347 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 40 2 40 2 76 2 10 2 (?)
a_n: 0 2 60 62 90 92 132 134 174 176 252 254 264 266
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: 266
Found by: Landjunge
db: batch=81, k=14, 58 28 40 40 76 10

TPT(14)	2154828833815432667	0 2 60 62 102 104 114 116 144 146 180 182 312 314	-1921189474680
STPT(10)	2154829348576920017	0 2 30 32 60 62 90 92 120 122	-1406427987330
STPT(10)	2154829420837319297	0 2 30 32 42 44 54 56 84 86	-1334167588050
STPT(10)	2154829665950330231	0 2 30 32 78 80 126 128 156 158	-1089054577116
SPT(16)	2154830083230416297	0 24 44 84 96 140 144 206 270 332 336 380 392 432 452 476	-671774491050
SPT(16)	2154830680444835623	0 40 48 88 90 118 154 174 250 270 306 334 336 376 384 424	-74560071724
SPT(16)	2154830978904996307	0 16 40 112 126 132 142 156 196 210 220 226 240 312 336 352	223900088960
SPT(16)	2154831816273034231	0 28 36 46 88 106 126 132 196 202 222 240 282 292 300 328	1061268126884
STPT(10)	2154832101970989209	0 2 18 20 30 32 42 44 60 62	1346966081862
SPT(16)	2154832225725883741	0 10 42 58 70 78 160 192 196 228 310 318 330 346 378 388	1470720976394
STPT(10)	2154832559848546997	0 2 12 14 42 44 72 74 84 86	1804843639650