Prime p₀= 2121325410154800761 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 76 2 58 2 10 2 124 2 28 2 (?)
a_n: 0 2 90 92 168 170 228 230 240 242 366 368 396 398
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: 398
Found by: Landjunge
db: batch=80, k=14, 88 76 58 10 124 28

SPT(16)	2121324915325409329	0 4 30 40 72 82 100 174 238 312 330 340 372 382 408 412	-494829391432
STPT(12)	2121324936040916717	0 2 12 14 42 44 72 74 102 104 114 116	-474113884044
SPT(16)	2121325039554678457	0 16 34 70 82 120 132 142 174 184 196 234 246 282 300 316	-370600122304
SPT(16)	2121325205577723811	0 18 28 102 108 130 136 168 190 222 228 250 256 330 340 358	-204577076950
SPT(16)	2121325205815245107	0 32 42 54 60 140 152 182 192 222 234 314 320 332 342 374	-204339555654
TPT(14)	2121325398446013029	0 2 48 50 90 92 138 140 180 182 312 314 462 464	-11708787732
STPT(10)	2121325832235741587	0 2 30 32 42 44 54 56 84 86	422080940826
SPT(16)	2121326042009510509	0 12 24 28 52 54 150 172 210 232 328 330 354 358 370 382	631854709748
STPT(10)	2121326198168052287	0 2 24 26 42 44 60 62 84 86	788013251526
SPT(16)	2121326604349167379	0 48 58 84 90 120 178 202 240 264 322 352 358 384 394 442	1194194366618
SPT(16)	2121326693675451019	0 18 24 52 114 142 220 234 238 252 330 358 420 448 454 472	1283520650258