Prime p₀= 2313358985887189727 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 52 2 16 2 76 2 70 2 40 2 (?)
a_n: 0 2 60 62 114 116 132 134 210 212 282 284 324 326
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: WTBroughton
db: batch=81, k=14, 58 52 16 76 70 40

SPT(16)	2313356692902758401	0 16 28 40 66 70 72 78 100 106 108 112 138 150 162 178	-2292984431326
SPT(16)	2313356927584757381	0 56 68 78 98 120 126 140 246 260 266 288 308 318 330 386	-2058302432346
SPT(16)	2313357872201111693	0 44 60 68 90 104 116 128 156 168 180 194 216 224 240 284	-1113686078034
SPT(16)	2313358301448956263	0 6 34 64 66 108 160 190 264 294 346 388 390 420 448 454	-684438233464
SPT(16)	2313358345219359307	0 22 34 52 60 94 154 174 190 210 270 304 312 330 342 364	-640667830420
STPT(10)	2313358904246912549	0 2 18 20 30 32 42 44 60 62	-81640277178
SPT(16)	2313359271549139097	0 36 44 56 72 110 114 116 180 182 186 224 240 252 260 296	285661949370
TPT(14)	2313359737154023091	0 2 18 20 48 50 78 80 228 230 330 332 396 398	751266833364
SPT(16)	2313359859479108393	0 18 48 98 116 128 150 156 218 224 246 258 276 326 356 374	873591918666
STPT(10)	2313359880726251387	0 2 30 32 60 62 90 92 120 122	894839061660
STPT(10)	2313360380308302077	0 2 30 32 42 44 54 56 84 86	1394421112350