Prime p₀= 2864786591878687079 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 46 2 10 2 28 2 34 2 (?)
a_n: 0 2 30 32 42 44 90 92 102 104 132 134 168 170
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]ATA-Rolf
db: batch=82, k=14, 28 10 46 10 28 34

SPT(16)	2864784868272515267	0 2 6 24 56 66 80 84 122 126 140 150 182 200 204 206	-1723606171812
SPT(16)	2864785101271035931	0 16 28 48 70 88 102 130 198 226 240 258 280 300 312 328	-1490607651148
TPT(14)	2864785415874001559	0 2 18 20 90 92 102 104 120 122 168 170 210 212	-1176004685520
SPT(16)	2864786133768714923	0 14 48 56 66 84 144 146 228 230 290 308 318 326 360 374	-458109972156
STPT(10)	2864786350406471927	0 2 60 62 102 104 144 146 204 206	-241472215152
STPT(10)	2864786493495339767	0 2 54 56 72 74 90 92 144 146	-98383347312
STPT(12)	2864786591878687079	0 2 30 32 42 44 90 92 102 104 132 134	0
STPT(10)	2864787065044450751	0 2 6 8 18 20 30 32 36 38	473165763672
SPT(16)	2864787090116987923	0 10 24 28 30 40 54 108 130 184 198 208 210 214 228 238	498238300844
SPT(16)	2864787166727056243	0 10 18 36 40 88 124 136 138 150 186 234 238 256 264 274	574848369164
SPT(16)	2864787248201686133	0 8 44 74 78 200 204 228 236 260 264 386 390 420 456 464	656322999054