Prime p₀= 2166415411428150809 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 76 2 58 2 76 2 88 2 22 2 (?)
a_n: 0 2 42 44 120 122 180 182 258 260 348 350 372 374
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: 374
Found by: ginga
db: batch=81, k=14, 40 76 58 76 88 22

SPT(16)	2166413681387241989	0 24 42 84 110 114 152 162 170 180 218 222 248 290 308 332	-1730040908820
SPT(16)	2166413905378549903	0 6 24 60 114 130 136 138 256 258 264 280 334 370 388 394	-1506049600906
SPT(16)	2166414439632392143	0 6 64 78 94 138 148 160 264 276 286 330 346 360 418 424	-971795758666
STPT(10)	2166414620257137779	0 2 12 14 90 92 168 170 180 182	-791171013030
STPT(10)	2166414998730710081	0 2 6 8 48 50 90 92 96 98	-412697440728
STPT(10)	2166415132650025391	0 2 36 38 78 80 120 122 156 158	-278778125418
SPT(16)	2166415547720281139	0 2 8 50 60 122 144 164 168 188 210 272 282 324 330 332	136292130330
SPT(16)	2166415645491807133	0 54 58 84 90 120 144 160 168 184 208 238 244 270 274 328	234063656324
STPT(10)	2166415877473297139	0 2 18 20 30 32 42 44 60 62	466045146330
SPT(16)	2166416031772197617	0 20 42 80 102 140 164 180 194 210 234 272 294 332 354 374	620344046808
SPT(16)	2166416056015531919	0 32 54 60 84 102 120 174 188 242 260 278 302 308 330 362	644587381110