Prime p₀= 2871397757318457377 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 4 2 100 2 40 2 58 2 34 2 (?)
a_n: 0 2 84 86 90 92 192 194 234 236 294 296 330 332
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: 332
Found by: Landjunge
db: batch=82, k=14, 82 4 100 40 58 34

SPT(16)	2871394177840546139	0 8 14 138 150 152 204 224 228 248 300 302 314 438 444 452	-3579477911238
SPT(20)	2871396007433058383	0 6 18 104 116 126 134 158 200 284 330 414 456 480 488 498 510 596 608 614	-1749885398994
SPT(16)	2871396272821949779	0 4 18 88 100 154 174 184 228 238 258 312 324 394 408 412	-1484496507598
STPT(10)	2871396535691971319	0 2 48 50 90 92 132 134 180 182	-1221626486058
STPT(10)	2871397091455415099	0 2 78 80 150 152 222 224 300 302	-665863042278
TPT(14)	2871397591801051967	0 2 12 14 42 44 54 56 84 86 90 92 132 134	-165517405410
STPT(10)	2871398084415348539	0 2 18 20 60 62 102 104 120 122	327096891162
SPT(18)	2871398309419292011	0 30 46 60 72 88 90 106 192 196 282 298 300 316 328 342 358 388	552100834634
SPT(16)	2871398383765024637	0 12 32 80 90 110 146 150 182 186 222 242 252 300 320 332	626446567260
STPT(10)	2871398559105875801	0 2 30 32 60 62 90 92 120 122	801787418424
SPT(16)	2871399102955687963	0 18 106 126 130 136 148 156 220 228 240 246 250 270 358 376	1345637230586