Prime p₀= 1538064954224314247 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 28 2 10 2 28 2 4 2 22 2 (?)
a_n: 0 2 12 14 42 44 54 56 84 86 90 92 114 116
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: 116
Found by: crashtech
db: batch=78, k=14, 10 28 10 28 4 22

SPT(18)	1538063633082745141	0 46 72 142 150 172 178 190 252 256 318 330 336 358 366 436 462 508	-1321141569106
SPT(16)	1538063680715965751	0 18 50 60 108 110 126 150 218 242 258 260 308 318 350 368	-1273508348496
SPT(16)	1538063906997575159	0 2 20 42 48 72 102 108 164 170 200 224 230 252 270 272	-1047226739088
SPT(16)	1538064535765841381	0 8 12 60 78 198 260 270 278 288 350 470 488 536 540 548	-418458472866
SPT(16)	1538064689722530667	0 34 40 66 96 102 136 172 174 210 244 250 280 306 312 346	-264501783580
SPT(16)	1538064851330127377	0 36 90 92 134 140 186 206 270 290 336 342 384 386 440 476	-102894186870
SPT(16)	1538065026788639287	0 12 22 46 72 100 102 126 226 250 252 280 306 330 340 352	72564325040
STPT(10)	1538065052952339029	0 2 18 20 30 32 42 44 60 62	98728024782
SPT(16)	1538065087131733241	0 56 60 78 126 156 168 186 212 230 242 272 320 338 342 398	132907418994
STPT(10)	1538065497253891421	0 2 6 8 48 50 90 92 96 98	543029577174
TPT(14)	1538065534701092567	0 2 84 86 102 104 120 122 132 134 144 146 174 176	580476778320