Prime p₀= 816429296644333751 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 4 2 28 2 40 2 46 2 10 2 (?)
a_n: 0 2 30 32 36 38 66 68 108 110 156 158 168 170
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: 170
Found by: [SG]FX
db: batch=73, k=14, 28 4 28 40 46 10

SPT(16)	816428272258956509	0 38 48 62 92 98 120 132 140 152 174 180 210 224 234 272	-1024385377242
STPT(10)	816428367388766651	0 2 30 32 78 80 126 128 156 158	-929255567100
SPT(16)	816428662555294301	0 2 6 108 122 132 156 210 248 302 326 336 350 452 456 458	-634089039450
SPT(16)	816428784392302909	0 10 22 24 90 112 120 150 172 202 210 232 298 300 312 322	-512252030842
STPT(12)	816428937976914917	0 2 72 74 90 92 252 254 270 272 342 344	-358667418834
STPT(10)	816428996456380091	0 2 36 38 78 80 120 122 156 158	-300187953660
SPT(16)	816429443446517209	0 4 24 58 72 78 130 144 148 162 214 220 234 268 288 292	146802183458
SPT(16)	816429475678840841	0 2 6 30 42 68 72 86 252 266 270 296 308 332 336 338	179034507090
STPT(10)	816429890460101507	0 2 42 44 72 74 102 104 144 146	593815767756
SPT(16)	816430052878202999	0 8 12 32 60 68 78 92 108 122 132 140 168 188 192 200	756233869248
STPT(10)	816430381032308459	0 2 18 20 30 32 42 44 60 62	1084387974708