Prime p₀= 2733467761135696589 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 58 2 166 2 28 2 40 2 34 2 (?)
a_n: 0 2 42 44 102 104 270 272 300 302 342 344 378 380
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: 380
Found by: JonS
db: batch=82, k=14, 40 58 166 28 40 34

SPT(16)	2733466831853933911	0 22 36 40 72 82 88 102 106 120 126 136 168 172 186 208	-929281762678
STPT(10)	2733466838598093779	0 2 18 20 30 32 42 44 60 62	-922537602810
SPT(16)	2733466993926761431	0 48 52 58 70 76 136 166 252 282 342 348 360 366 370 418	-767208935158
SPT(16)	2733467178401580017	0 12 56 96 152 182 192 206 276 290 300 330 386 426 470 482	-582734116572
SPT(16)	2733467362848384179	0 8 42 72 90 122 150 162 260 272 300 332 350 380 414 422	-398287312410
SPT(16)	2733467388969563963	0 6 56 68 110 120 134 156 188 210 224 234 276 288 338 344	-372166132626
STPT(10)	2733468405298615727	0 2 12 14 42 44 72 74 84 86	644162919138
SPT(20)	2733468517563998251	0 46 78 88 90 102 112 148 156 162 226 232 240 276 286 298 300 310 342 388	756428301662
STPT(10)	2733468649065393917	0 2 30 32 42 44 54 56 84 86	887929697328
STPT(10)	2733468785383392179	0 2 12 14 30 32 48 50 60 62	1024247695590
STPT(10)	2733469227971673869	0 2 18 20 30 32 42 44 60 62	1466835977280