Prime p₀= 234891511979197781 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 88 2 34 2 82 2 34 2 40 2 (?)
a_n: 0 2 30 32 120 122 156 158 240 242 276 278 318 320
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: 320
Found by: Megacruncher
db: batch=69, k=14, 28 88 34 82 34 40

TPT(12)	234891441033809381	0 2 108 110 126 128 150 152 288 290 378 380	-70945388400
SPT(14)	234891444917776709	0 12 20 72 90 102 122 132 152 164 182 234 242 254	-67061421072
SPT(14)	234891447892271021	0 12 42 80 140 146 176 192 222 228 288 326 356 368	-64086926760
SPT(14)	234891460393948361	0 50 56 78 108 138 150 236 248 278 308 330 336 386	-51585249420
SPT(14)	234891472929363559	0 18 58 60 82 112 130 192 210 240 262 264 304 322	-39049834222
SPT(14)	234891500500582033	0 64 66 70 94 120 136 168 184 210 234 238 240 304	-11478615748
SPT(14)	234891519221309603	0 50 60 90 104 126 134 156 164 186 200 230 240 290	7242111822
TPT(14)	234891527133472217	0 2 24 26 72 74 150 152 162 164 192 194 222 224	15154274436
SPT(14)	234891529275852193	0 16 24 28 40 54 94 210 250 264 276 280 288 304	17296654412
SPT(14)	234891536621068211	0 8 30 42 68 120 152 156 188 240 266 278 300 308	24641870430
SPT(14)	234891541578691493	0 60 84 104 138 144 188 276 320 326 360 380 404 464	29599493712