Prime p₀= 2597756078417407769 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 16 2 46 2 28 2 28 2 22 2 (?)
a_n: 0 2 12 14 30 32 78 80 108 110 138 140 162 164
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: 164
Found by: Orange Kid
db: batch=82, k=14, 10 16 46 28 28 22

SPT(16)	2597752319014468001	0 2 12 42 50 66 72 78 170 176 182 198 206 236 246 248	-3759402939768
SPT(20)	2597752336575039283	0 48 58 66 70 78 96 100 138 148 168 178 216 220 238 246 250 258 268 316	-3741842368486
STPT(10)	2597753738224581059	0 2 12 14 30 32 48 50 60 62	-2340192826710
SPT(16)	2597754976418132407	0 30 34 52 64 76 132 136 210 214 270 282 294 312 316 346	-1101999275362
SPT(16)	2597755074917877403	0 6 34 40 64 124 154 166 198 210 240 300 324 330 358 364	-1003499530366
SPT(16)	2597755763985256489	0 18 30 42 52 60 88 94 108 114 142 150 160 172 184 202	-314432151280
STPT(10)	2597756344516962491	0 2 36 38 78 80 120 122 156 158	266099554722
SPT(16)	2597756676143364821	0 38 42 138 152 182 186 210 218 242 246 276 290 386 390 428	597725957052
SPT(16)	2597757060996092399	0 8 18 60 132 144 164 188 264 288 308 320 392 434 444 452	982578684630
SPT(16)	2597757368681308523	0 18 44 84 104 170 200 224 354 378 408 474 494 534 560 578	1290263900754
STPT(10)	2597757464549538827	0 2 30 32 42 44 54 56 84 86	1386132131058