Prime p₀= 2566547533684101659 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 100 2 4 2 40 2 28 2 16 2 22 2 (?)
a_n: 0 2 102 104 108 110 150 152 180 182 198 200 222 224
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: 224
Found by: Ben
db: batch=82, k=14, 100 4 40 28 16 22

SPT(16)	2566545866875276843	0 18 46 58 88 100 120 156 160 196 216 228 258 270 298 316	-1666808824816
SPT(13)	2566546562030998567	0 12 30 54 72 114 132 150 192 210 234 252 264	-971653103092
SPT(16)	2566546806121703659	0 42 72 150 204 210 220 262 372 414 424 430 484 562 592 634	-727562398000
TPT(14)	2566546917391604417	0 2 12 14 54 56 90 92 114 116 180 182 210 212	-616292497242
SPT(16)	2566547156104931011	0 48 78 90 112 136 138 160 168 190 192 216 238 250 280 328	-377579170648
STPT(10)	2566547465408875307	0 2 60 62 102 104 144 146 204 206	-68275226352
SPT(16)	2566548074931670307	0 36 86 150 170 186 192 230 312 350 356 372 392 456 506 542	541247568648
STPT(10)	2566548133135477259	0 2 18 20 30 32 42 44 60 62	599451375600
STPT(10)	2566548959904768731	0 2 6 8 48 50 90 92 96 98	1426220667072
SPT(18)	2566549326478514483	0 18 54 74 78 84 138 156 170 234 248 266 320 326 330 350 386 404	1792794412824
SPT(16)	2566549360777287323	0 6 78 138 176 218 230 320 324 414 426 468 506 566 638 644	1827093185664