Prime p₀= 2913678676958825597 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 58 2 4 2 28 2 10 2 28 2 (?)
a_n: 0 2 24 26 84 86 90 92 120 122 132 134 162 164
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: 164
Found by: Orange Kid
db: batch=82, k=14, 22 58 4 28 10 28

STPT(10)	2913676950534920807	0 2 30 32 42 44 54 56 84 86	-1726423904790
SPT(16)	2913677760893461213	0 4 18 66 94 168 198 210 214 226 256 330 358 406 420 424	-916065364384
STPT(10)	2913678174222571331	0 2 36 38 78 80 120 122 156 158	-502736254266
SPT(16)	2913678316431659317	0 24 90 102 132 136 156 160 186 190 210 214 244 256 322 346	-360527166280
SPT(16)	2913678359307338041	0 58 60 130 160 168 222 250 300 328 382 390 420 490 492 550	-317651487556
SPT(16)	2913678665666914253	0 8 20 30 38 44 80 98 120 138 174 180 188 198 210 218	-11291911344
STPT(10)	2913679116826318829	0 2 18 20 30 32 42 44 60 62	439867493232
STPT(10)	2913679339712194379	0 2 18 20 30 32 42 44 60 62	662753368782
SPT(16)	2913679355680897519	0 4 72 78 88 100 108 112 150 154 162 174 184 190 258 262	678722071922
SPT(16)	2913679358947265879	0 20 42 104 122 132 168 192 200 224 260 270 288 350 372 392	681988440282
SPT(16)	2913679596046814879	0 98 140 162 170 174 204 240 242 278 308 312 320 342 384 482	919087989282