Prime p₀= 2878722271420876709 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 112 2 4 2 10 2 70 2 34 2 (?)
a_n: 0 2 48 50 162 164 168 170 180 182 252 254 288 290
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: 290
Found by: Landjunge
db: batch=82, k=14, 46 112 4 10 70 34

SPT(16)	2878720354703169037	0 66 166 172 190 204 216 222 244 250 262 276 294 300 400 466	-1916717707672
SPT(16)	2878720665719244491	0 6 80 120 126 140 176 192 200 216 252 266 272 312 386 392	-1605701632218
STPT(10)	2878720792357808477	0 2 72 74 102 104 132 134 204 206	-1479063068232
SPT(16)	2878721543854242157	0 4 10 22 54 60 64 82 84 102 106 112 144 156 162 166	-727566634552
STPT(10)	2878721885248567409	0 2 78 80 120 122 162 164 240 242	-386172309300
SPT(16)	2878722216994379207	0 14 30 60 162 200 212 222 284 294 306 344 446 476 492 506	-54426497502
SPT(16)	2878722389919183853	0 24 106 114 154 156 160 190 210 240 244 246 286 294 376 400	118498307144
SPT(16)	2878722413600523601	0 90 118 150 156 198 216 222 256 262 280 322 328 360 388 478	142179646892
STPT(10)	2878722569063477837	0 2 30 32 42 44 54 56 84 86	297642601128
STPT(10)	2878722753709953089	0 2 42 44 60 62 78 80 120 122	482289076380
STPT(10)	2878723045904842217	0 2 42 44 72 74 102 104 144 146	774483965508