Prime p₀= 2829646372010356781 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 196 2 28 2 22 2 34 2 130 2 (?)
a_n: 0 2 78 80 276 278 306 308 330 332 366 368 498 500
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: 500
Found by: JayPi
db: batch=82, k=14, 76 196 28 22 34 130

SPT(16)	2829644134726055567	0 30 42 56 60 86 180 182 384 386 480 506 510 524 536 566	-2237284301214
STPT(10)	2829644667787525277	0 2 30 32 42 44 54 56 84 86	-1704222831504
SPT(16)	2829644923394259833	0 36 48 80 108 146 156 210 254 308 318 356 384 416 428 464	-1448616096948
SPT(16)	2829644949316620707	0 44 86 90 164 174 180 194 252 266 272 282 356 360 402 446	-1422693736074
STPT(12)	2829646099161119969	0 2 42 44 90 92 162 164 210 212 252 254	-272849236812
STPT(10)	2829646295493198029	0 2 30 32 60 62 90 92 120 122	-76517158752
STPT(10)	2829646519584175259	0 2 42 44 90 92 138 140 180 182	147573818478
STPT(10)	2829646731225306437	0 2 30 32 42 44 54 56 84 86	359214949656
SPT(16)	2829647132519326159	0 24 34 54 78 94 138 154 174 190 234 250 274 294 304 328	760508969378
STPT(10)	2829647132588155907	0 2 30 32 42 44 54 56 84 86	760577799126
STPT(10)	2829647927360997539	0 2 18 20 30 32 42 44 60 62	1555350640758