Prime p₀= 2732295351571342757 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 22 2 34 2 22 2 106 2 208 2 (?)
a_n: 0 2 30 32 54 56 90 92 114 116 222 224 432 434
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: 434
Found by: Ben
db: batch=82, k=14, 28 22 34 22 106 208

SPT(16)	2732295086144489093	0 44 54 98 114 170 174 176 258 260 264 320 336 380 390 434	-265426853664
STPT(10)	2732295116126396069	0 2 18 20 30 32 42 44 60 62	-235444946688
SPT(16)	2732295157497863707	0 12 22 36 72 96 112 136 210 234 250 274 310 324 334 346	-194073479050
SPT(16)	2732295213667881493	0 4 30 48 114 118 168 234 364 430 480 484 550 568 594 598	-137903461264
STPT(10)	2732295321939067901	0 2 30 32 78 80 126 128 156 158	-29632274856
STPT(10)	2732295336159205511	0 2 36 38 78 80 120 122 156 158	-15412137246
SPT(16)	2732295877630452389	0 2 44 62 90 102 132 188 324 380 410 422 450 468 510 512	526059109632
SPT(16)	2732296315655170871	0 18 26 32 36 62 66 78 80 92 96 122 126 132 140 158	964083828114
SPT(16)	2732296671390815857	0 4 40 42 52 66 136 160 186 210 280 294 304 306 342 346	1319819473100
STPT(10)	2732296673819544191	0 2 6 8 48 50 90 92 96 98	1322248201434
SPT(16)	2732297682042460033	0 34 36 60 76 88 124 186 238 300 336 348 364 388 390 424	2330471117276