Prime p₀= 4506240508728734927 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 10 2 10 2 28 2 16 2 (?)
a_n: 0 2 30 32 60 62 72 74 84 86 114 116 132 134
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: 134
Found by: Stony666
db: batch=85, k=14, 28 28 10 10 28 16

SPT(16)	4506239176832154263	0 38 66 80 104 134 144 150 344 350 360 390 414 428 456 494	-1331896580664
TPT(14)	4506239479148390237	0 2 72 74 90 92 102 104 132 134 204 206 282 284	-1029580344690
SPT(16)	4506239510490792289	0 10 18 28 42 90 112 118 144 150 172 220 234 244 252 262	-998237942638
STPT(10)	4506239516512572869	0 2 18 20 30 32 42 44 60 62	-992216162058
SPT(16)	4506239636849556797	0 14 32 50 66 74 90 102 104 116 132 140 156 174 192 206	-871879178130
TPT(14)	4506239774203938269	0 2 30 32 72 74 78 80 90 92 132 134 198 200	-734524796658
STPT(10)	4506240508728734957	0 2 30 32 42 44 54 56 84 86	30
SPT(16)	4506240569342026421	0 2 56 96 102 152 158 168 200 210 216 266 272 312 366 368	60613291494
SPT(16)	4506240613437823093	0 18 28 58 60 78 124 130 204 210 256 274 276 306 316 334	104709088166
STPT(10)	4506241224729224081	0 2 6 8 48 50 90 92 96 98	716000489154
SPT(16)	4506241361043087581	0 2 56 80 122 152 182 192 230 240 270 300 342 366 420 422	852314352654