Prime p₀= 2086381577463585971 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 124 2 28 2 28 2 40 2 10 2 (?)
a_n: 0 2 30 32 156 158 186 188 216 218 258 260 270 272
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: 272
Found by: Landjunge
db: batch=80, k=14, 28 124 28 28 40 10

SPT(16)	2086380587412666443	0 8 20 98 120 134 150 164 174 188 204 218 240 318 330 338	-990050919528
STPT(10)	2086380770666403527	0 2 30 32 42 44 54 56 84 86	-806797182444
STPT(10)	2086381114758527681	0 2 6 8 48 50 90 92 96 98	-462705058290
STPT(10)	2086381408863393581	0 2 30 32 60 62 90 92 120 122	-168600192390
SPT(16)	2086381462355053121	0 18 42 90 188 192 200 228 272 300 308 312 410 458 482 500	-115108532850
TPT(14)	2086381500022181441	0 2 48 50 78 80 120 122 156 158 186 188 336 338	-77441404530
SPT(16)	2086381755534704389	0 82 94 100 102 144 234 240 292 298 388 430 432 438 450 532	178071118418
STPT(10)	2086382235992036819	0 2 48 50 90 92 132 134 180 182	658528450848
SPT(16)	2086382297333262529	0 52 60 102 112 160 172 198 214 240 252 300 310 352 360 412	719869676558
STPT(10)	2086382728746190241	0 2 6 8 48 50 90 92 96 98	1151282604270
SPT(16)	2086382779076463341	0 48 80 102 108 126 132 162 206 236 242 260 266 288 320 368	1201612877370