Prime p₀= 2954093562400725881 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 28 2 10 2 10 2 76 2 40 2 (?)
a_n: 0 2 36 38 66 68 78 80 90 92 168 170 210 212
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: 212
Found by: ginga
db: batch=82, k=14, 34 28 10 10 76 40

SPT(16)	2954092012531492223	0 74 80 84 108 140 146 174 200 228 234 266 290 294 300 374	-1549869233658
SPT(16)	2954092184785177133	0 36 54 96 158 176 206 246 308 348 378 396 458 500 518 554	-1377615548748
SPT(16)	2954092208900536463	0 30 48 50 74 78 84 90 128 134 140 144 168 170 188 218	-1353500189418
STPT(10)	2954092843648159877	0 2 42 44 72 74 102 104 144 146	-718752566004
SPT(16)	2954093448172206541	0 22 36 66 106 108 112 138 160 186 190 192 232 262 276 298	-114228519340
SPT(16)	2954093541416929591	0 10 12 16 42 70 72 82 180 190 192 220 246 250 252 262	-20983796290
SPT(13)	2954094492713260363	0 18 90 174 180 210 264 318 348 354 438 510 528	930312534482
SPT(16)	2954094970553440453	0 24 70 78 94 120 138 168 256 286 304 330 346 354 400 424	1408152714572
SPT(16)	2954095173233373931	0 6 46 72 82 102 126 132 136 142 166 186 196 222 262 268	1610832648050
STPT(10)	2954095603590279821	0 2 30 32 78 80 126 128 156 158	2041189553940
SPT(16)	2954095672277450483	0 24 26 66 84 96 104 110 180 186 194 206 224 264 266 290	2109876724602