Prime p₀= 2316538781210071421 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 118 2 28 2 28 2 94 2 28 2 22 2 (?)
a_n: 0 2 120 122 150 152 180 182 276 278 306 308 330 332
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: 332
Found by: JonS
db: batch=81, k=14, 118 28 28 94 28 22

SPT(16)	2316537558949109407	0 22 30 36 66 84 94 106 120 132 142 160 190 196 204 226	-1222260962014
STPT(10)	2316537607149160691	0 2 6 8 18 20 30 32 36 38	-1174060910730
STPT(10)	2316537964504473947	0 2 30 32 42 44 54 56 84 86	-816705597474
SPT(16)	2316538243577814301	0 16 22 100 108 178 222 282 286 346 390 460 468 546 552 568	-537632257120
SPT(16)	2316538555449178187	0 36 66 80 96 110 116 140 222 246 252 266 282 296 326 362	-225760893234
SPT(16)	2316538620809792387	0 26 60 66 74 86 110 164 186 240 264 276 284 290 324 350	-160400279034
STPT(10)	2316538947086330567	0 2 42 44 72 74 102 104 144 146	165876259146
STPT(10)	2316539019821483801	0 2 36 38 78 80 120 122 156 158	238611412380
STPT(10)	2316539128158743627	0 2 42 44 72 74 102 104 144 146	346948672206
SPT(16)	2316539140523812441	0 18 40 42 58 66 100 108 130 138 172 180 196 198 220 238	359313741020
SPT(16)	2316539293332860879	0 2 8 24 38 48 50 162 260 372 374 384 398 414 420 422	512122789458