Prime p₀= 2539993346562771557 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 40 2 34 2 10 2 40 2 28 2 (?)
a_n: 0 2 42 44 84 86 120 122 132 134 174 176 204 206
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: 206
Found by: JayPi
db: batch=82, k=14, 40 40 34 10 40 28

SPT(16)	2539991883338606819	0 12 14 24 30 68 108 132 170 194 234 272 278 288 290 302	-1463224164738
STPT(10)	2539991938912429889	0 2 18 20 30 32 42 44 60 62	-1407650341668
SPT(16)	2539992084470399891	0 48 56 66 80 90 92 140 198 246 248 258 272 282 290 338	-1262092371666
STPT(10)	2539992550798180727	0 2 30 32 42 44 54 56 84 86	-795764590830
SPT(16)	2539992588867004021	0 66 78 142 148 150 156 186 202 232 238 240 246 310 322 388	-757695767536
SPT(16)	2539992962867305651	0 46 208 210 222 276 280 298 300 318 322 376 388 390 552 598	-383695465906
SPT(16)	2539993416317880511	0 18 36 76 108 118 130 150 238 258 270 280 312 352 370 388	69755108954
SPT(16)	2539993799249344049	0 44 50 54 62 120 138 140 162 164 182 240 248 252 258 302	452686572492
SPT(16)	2539994057871467293	0 28 66 126 150 178 180 186 280 286 288 316 340 400 438 466	711308695736
SPT(16)	2539994770516795763	0 36 66 78 80 90 96 120 224 248 254 264 266 278 308 344	1423954024206
STPT(10)	2539995029892677057	0 2 30 32 42 44 54 56 84 86	1683329905500