Prime p₀= 2322886403704026707 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 64 2 58 2 70 2 28 2 76 2 (?)
a_n: 0 2 54 56 120 122 180 182 252 254 282 284 360 362
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: 362
Found by: MarkRBright
db: batch=81, k=14, 52 64 58 70 28 76

SPT(16)	2322885639856005899	0 8 12 30 38 78 120 140 162 182 224 264 272 290 294 302	-763848020808
SPT(16)	2322885841474361209	0 4 118 132 148 180 190 204 208 222 232 264 280 294 408 412	-562229665498
STPT(10)	2322885998497481411	0 2 36 38 78 80 120 122 156 158	-405206545296
TPT(14)	2322886089150827489	0 2 48 50 78 80 120 122 240 242 282 284 288 290	-314553199218
STPT(10)	2322886220534772437	0 2 30 32 42 44 54 56 84 86	-183169254270
SPT(16)	2322886377189277261	0 18 22 112 120 162 238 250 258 270 346 388 396 486 490 508	-26514749446
STPT(10)	2322886471560858989	0 2 42 44 60 62 78 80 120 122	67856832282
SPT(13)	2322886537627783063	0 30 60 96 180 186 198 210 216 300 336 366 396	133923756356
STPT(10)	2322887242823985977	0 2 12 14 42 44 72 74 84 86	839119959270
SPT(16)	2322887953828200637	0 22 40 90 112 132 172 190 222 240 280 300 322 372 390 412	1550124173930
STPT(10)	2322888309599563241	0 2 6 8 48 50 90 92 96 98	1905895536534