Prime p₀= 2126371659482844041 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 10 2 118 2 40 2 28 2 58 2 (?)
a_n: 0 2 36 38 48 50 168 170 210 212 240 242 300 302
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: 302
Found by: Landjunge
db: batch=80, k=14, 34 10 118 40 28 58

SPT(16)	2126370618972493021	0 10 22 66 72 76 126 156 196 226 276 280 286 330 342 352	-1040510351020
STPT(10)	2126370657001249541	0 2 36 38 78 80 120 122 156 158	-1002481594500
SPT(16)	2126370929859519731	0 12 38 68 86 108 122 180 278 336 350 372 390 420 446 458	-729623324310
STPT(10)	2126371010222362229	0 2 18 20 30 32 42 44 60 62	-649260481812
SPT(16)	2126371202465180599	0 12 22 42 60 120 148 192 250 294 322 382 400 420 430 442	-457017663442
STPT(10)	2126371300179430349	0 2 12 14 90 92 168 170 180 182	-359303413692
SPT(16)	2126372199728356793	0 36 48 54 56 98 104 110 114 120 126 168 170 176 188 224	540245512752
SPT(16)	2126372363038749367	0 12 40 54 64 72 100 120 154 174 202 210 220 234 262 274	703555905326
SPT(16)	2126372556041398543	0 4 16 30 90 114 118 120 154 156 160 184 244 258 270 274	896558554502
STPT(10)	2126372685360610637	0 2 30 32 42 44 54 56 84 86	1025877766596
STPT(10)	2126372927999685941	0 2 36 38 78 80 120 122 156 158	1268516841900