Prime p₀= 1025564040625671431 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 148 2 58 2 4 2 70 2 16 2 22 2 (?)
a_n: 0 2 150 152 210 212 216 218 288 290 306 308 330 332
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: HenkM
db: batch=76, k=14, 148 58 4 70 16 22

STPT(10)	1025563259158326737	0 2 30 32 60 62 90 92 120 122	-781467344694
STPT(10)	1025563447063939829	0 2 48 50 90 92 132 134 180 182	-593561731602
STPT(10)	1025563518199587467	0 2 42 44 72 74 102 104 144 146	-522426083964
SPT(16)	1025563621325757671	0 48 72 110 120 188 212 240 320 348 372 440 450 488 512 560	-419299913760
SPT(16)	1025563744276464353	0 6 36 56 80 108 158 186 230 258 308 336 360 380 410 416	-296349207078
STPT(10)	1025563914264387479	0 2 18 20 60 62 102 104 120 122	-126361283952
SPT(16)	1025564223484101317	0 14 20 44 86 132 134 170 216 252 254 300 342 366 372 386	182858429886
SPT(16)	1025564237951818907	0 6 26 30 44 116 170 180 200 210 264 336 350 354 374 380	197326147476
SPT(16)	1025564780999824487	0 2 44 116 126 132 164 174 182 192 224 230 240 312 354 356	740374153056
SPT(16)	1025565056773695077	0 2 12 24 84 110 150 170 234 254 294 320 380 392 402 404	1016148023646
SPT(16)	1025565119842604183	0 6 24 38 50 68 150 156 188 194 276 294 306 320 338 344	1079216932752