Prime p₀= 2310453354771226391 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 64 2 10 2 70 2 94 2 58 2 (?)
a_n: 0 2 60 62 126 128 138 140 210 212 306 308 366 368
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: 368
Found by: Orange Kid
db: batch=81, k=14, 58 64 10 70 94 58

SPT(16)	2310451074924690727	0 54 60 84 94 102 112 130 186 204 214 222 232 256 262 316	-2279846535664
STPT(10)	2310451125640766369	0 2 48 50 60 62 72 74 120 122	-2229130460022
SPT(16)	2310452150757604081	0 16 46 48 82 88 100 126 172 198 210 216 250 252 282 298	-1204013622310
SPT(16)	2310452660078888111	0 42 92 98 140 146 152 198 230 276 282 288 330 336 386 428	-694692338280
SPT(16)	2310453170273299313	0 8 38 56 80 84 108 114 140 146 170 174 198 216 246 254	-184497927078
STPT(10)	2310453268545793907	0 2 30 32 42 44 54 56 84 86	-86225432484
STPT(10)	2310453599618966441	0 2 6 8 48 50 90 92 96 98	244847740050
SPT(16)	2310454191693193291	0 6 48 70 82 132 148 172 246 270 286 336 348 370 412 418	836921966900
SPT(16)	2310454500542012819	0 12 14 54 60 68 98 140 222 264 294 302 308 348 350 362	1145770786428
SPT(16)	2310454804372704911	0 6 12 18 36 42 50 62 96 108 116 122 140 146 152 158	1449601478520
STPT(10)	2310455098829582447	0 2 12 14 42 44 72 74 84 86	1744058356056