Prime p₀= 812538805387373681 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 88 2 28 2 40 2 10 2 34 2 (?)
a_n: 0 2 36 38 126 128 156 158 198 200 210 212 246 248
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: 248
Found by: [SG]FX
db: batch=73, k=14, 34 88 28 40 10 34

SPT(18)	812536650990906539	0 8 32 42 60 110 120 140 174 188 222 242 252 302 320 330 354 362	-2154396467142
SPT(16)	812536679261942749	0 10 28 48 72 78 100 102 160 162 184 190 214 234 252 262	-2126125430932
TPT(14)	812536715239290047	0 2 12 14 84 86 222 224 240 242 264 266 420 422	-2090148083634
TPT(14)	812537406720699347	0 2 72 74 84 86 114 116 240 242 312 314 330 332	-1398666674334
TPT(14)	812538068535740381	0 2 48 50 90 92 228 230 246 248 468 470 546 548	-736851633300
STPT(10)	812538747132714629	0 2 18 20 30 32 42 44 60 62	-58254659052
STPT(10)	812538979202631137	0 2 30 32 72 74 114 116 144 146	173815257456
SPT(16)	812539115363624689	0 18 22 28 82 138 150 154 228 232 244 300 354 360 364 382	309976251008
STPT(10)	812539739382360641	0 2 36 38 78 80 120 122 156 158	933994986960
STPT(10)	812539952216280887	0 2 30 32 42 44 54 56 84 86	1146828907206
SPT(16)	812540071115075543	0 30 60 66 80 104 144 168 206 230 270 294 308 314 344 374	1265727701862