Prime p₀= 2312334193102453061 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 10 2 70 2 46 2 130 2 28 2 (?)
a_n: 0 2 36 38 48 50 120 122 168 170 300 302 330 332
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: 332
Found by: JonS
db: batch=81, k=14, 34 10 70 46 130 28

TPT(14)	2312331307113076157	0 2 54 56 84 86 234 236 240 242 282 284 294 296	-2885989376904
SPT(16)	2312332189570385891	0 30 32 56 60 62 132 198 200 266 336 338 342 366 368 398	-2003532067170
SPT(16)	2312332281857602261	0 22 28 48 76 118 160 192 256 288 330 372 400 420 426 448	-1911244850800
SPT(16)	2312332615148961043	0 34 48 58 64 126 130 144 160 174 178 240 246 256 270 304	-1577953492018
SPT(16)	2312332994322260699	0 14 20 98 102 110 152 164 258 270 312 320 324 402 408 422	-1198780192362
SPT(16)	2312333811704712007	0 130 132 142 154 160 192 196 300 304 336 342 354 364 366 496	-381397741054
SPT(16)	2312334216055715941	0 12 48 60 70 78 88 102 148 162 172 180 190 202 238 250	22953262880
SPT(16)	2312334414106739249	0 38 68 80 104 122 252 278 294 320 450 468 492 504 534 572	221004286188
STPT(10)	2312334428609060039	0 2 18 20 30 32 42 44 60 62	235506606978
SPT(18)	2312334665094931627	0 10 40 72 112 132 150 154 156 220 222 226 244 264 304 336 366 376	471992478566
SPT(18)	2312334844587988211	0 8 26 60 68 90 98 116 146 180 210 228 236 258 266 300 318 326	651485535150