Prime p₀= 2964940491532621697 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 154 2 40 2 10 2 34 2 22 2 (?)
a_n: 0 2 54 56 210 212 252 254 264 266 300 302 324 326
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: 326
Found by: Roadranner
db: batch=82, k=14, 52 154 40 10 34 22

SPT(16)	2964939887407313279	0 2 18 24 38 44 72 80 192 200 228 234 248 254 270 272	-604125308418
SPT(16)	2964939961036257613	0 6 16 36 58 84 114 120 154 160 190 216 238 258 268 274	-530496364084
SPT(16)	2964940207821973531	0 22 28 30 112 118 120 142 168 190 192 198 280 282 288 310	-283710648166
STPT(10)	2964940225377010337	0 2 30 32 72 74 114 116 144 146	-266155611360
SPT(16)	2964940321710837383	0 20 26 56 78 114 146 156 158 168 200 236 258 288 294 314	-169821784314
TPT(14)	2964940427673082517	0 2 24 26 114 116 150 152 222 224 240 242 360 362	-63859539180
SPT(16)	2964940550621176753	0 16 36 90 94 150 168 174 220 226 244 300 304 358 378 394	59088555056
SPT(16)	2964940601197259681	0 8 62 68 80 98 122 162 236 276 300 318 330 336 390 398	109664637984
SPT(16)	2964940702154347001	0 2 30 38 50 56 68 108 140 180 192 198 210 218 246 248	210621725304
STPT(10)	2964940905107668787	0 2 24 26 42 44 60 62 84 86	413575047090
SPT(16)	2964941016202396813	0 4 24 30 40 54 58 84 124 150 154 168 178 184 204 208	524669775116