Prime p₀= 798816381528673661 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 34 2 40 2 28 2 10 2 (?)
a_n: 0 2 30 32 60 62 96 98 138 140 168 170 180 182
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: 182
Found by: [SG-2W]Kurzer
db: batch=73, k=14, 28 28 34 40 28 10

SPT(16)	798815361973359671	0 20 110 128 162 168 188 210 218 240 260 266 300 318 408 428	-1019555313990
STPT(10)	798815553557852861	0 2 30 32 60 62 90 92 120 122	-827970820800
SPT(18)	798815640478501021	0 10 78 82 88 150 160 190 252 298 360 390 400 462 468 472 540 550	-741050172640
SPT(16)	798815824621564021	0 28 30 42 48 60 76 82 186 192 208 220 226 238 240 268	-556907109640
SPT(16)	798816115285459871	0 12 20 42 48 78 92 98 132 138 152 182 188 210 218 230	-266243213790
SPT(16)	798816219050505137	0 6 14 20 26 62 86 144 152 210 234 270 276 282 290 296	-162478168524
STPT(10)	798816649520359367	0 2 42 44 102 104 162 164 204 206	267991685706
SPT(16)	798816827007097663	0 18 30 58 64 66 114 150 154 190 238 240 246 274 286 304	445478424002
SPT(16)	798816997202966519	0 18 50 74 110 114 162 182 240 260 308 312 348 372 404 422	615674292858
STPT(10)	798817196679831809	0 2 18 20 30 32 42 44 60 62	815151158148
STPT(10)	798817345806609599	0 2 42 44 120 122 198 200 240 242	964277935938