Prime p₀= 2726260031288736557 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 100 2 118 2 16 2 22 2 28 2 16 2 (?)
a_n: 0 2 102 104 222 224 240 242 264 266 294 296 312 314
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: 314
Found by: raddoc
db: batch=82, k=14, 100 118 16 22 28 16

SPT(16)	2726258799089628091	0 18 46 58 60 142 148 160 198 210 216 298 300 312 340 358	-1232199108466
SPT(16)	2726259056050395113	0 8 54 84 96 108 150 156 218 224 266 278 290 320 366 374	-975238341444
STPT(10)	2726259190107522437	0 2 30 32 42 44 54 56 84 86	-841181214120
SPT(16)	2726259205829815741	0 16 30 42 46 52 60 82 156 178 186 192 196 208 222 238	-825458920816
SPT(16)	2726259521448971021	0 92 126 140 152 170 176 182 246 252 258 276 288 302 336 428	-509839765536
SPT(16)	2726259577385553787	0 12 22 36 40 70 100 132 154 186 216 246 250 264 274 286	-453903182770
STPT(10)	2726260235836066751	0 2 6 8 48 50 90 92 96 98	204547330194
SPT(16)	2726260372534051079	0 12 62 72 74 84 114 150 314 350 380 390 392 402 452 464	341245314522
STPT(10)	2726260456659554387	0 2 24 26 42 44 60 62 84 86	425370817830
SPT(16)	2726260514730137621	0 36 48 78 90 92 122 132 176 186 216 218 230 260 272 308	483441401064
STPT(10)	2726260668281572859	0 2 48 50 90 92 132 134 180 182	636992836302