Prime p₀= 820142808126023267 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 10 2 58 2 58 2 64 2 10 2 (?)
a_n: 0 2 42 44 54 56 114 116 174 176 240 242 252 254
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: 254
Found by: Theadalus
db: batch=73, k=14, 40 10 58 58 64 10

STPT(10)	820141911614464247	0 2 12 14 72 74 132 134 144 146	-896511559020
SPT(16)	820141994946727379	0 12 42 62 80 84 92 114 188 210 218 222 240 260 290 302	-813179295888
SPT(16)	820142367888724781	0 6 26 66 68 98 102 116 132 146 150 180 182 222 242 248	-440237298486
STPT(10)	820142469360174209	0 2 18 20 30 32 42 44 60 62	-338765849058
SPT(16)	820142540579629271	0 8 26 36 42 110 140 156 242 258 288 356 362 372 390 398	-267546393996
SPT(16)	820142753642748229	0 40 42 72 82 114 168 172 180 184 238 270 280 310 312 352	-54483275038
SPT(16)	820143097179516667	0 12 22 34 60 64 72 90 196 214 222 226 252 264 274 286	289053493400
STPT(10)	820143296312422601	0 2 36 38 78 80 120 122 156 158	488186399334
STPT(10)	820143318542291501	0 2 6 8 18 20 30 32 36 38	510416268234
STPT(10)	820143702966902099	0 2 42 44 120 122 198 200 240 242	894840878832
SPT(16)	820143944277874331	0 12 20 26 42 62 90 98 120 128 156 176 192 198 206 218	1136151851064