Prime p₀= 2574445541187779471 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 16 2 10 2 28 2 88 2 34 2 (?)
a_n: 0 2 60 62 78 80 90 92 120 122 210 212 246 248
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: 248
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 58 16 10 28 88 34

STPT(12)	2574444106001494367	0 2 12 14 54 56 60 62 102 104 114 116	-1435186285104
SPT(16)	2574444331311823129	0 130 150 202 262 294 334 360 364 390 430 462 522 574 594 724	-1209875956342
SPT(16)	2574444360543551257	0 54 172 256 270 292 312 334 342 364 384 406 420 504 622 676	-1180644228214
SPT(16)	2574444468845978009	0 8 14 24 138 152 168 180 182 194 210 224 338 348 354 362	-1072341801462
SPT(16)	2574444605270838031	0 40 76 102 130 132 216 250 288 322 406 408 436 462 498 538	-935916941440
SPT(16)	2574444852673333141	0 10 42 60 88 108 132 138 160 166 190 210 238 256 288 298	-688514446330
STPT(10)	2574445577900045807	0 2 24 26 42 44 60 62 84 86	36712266336
SPT(16)	2574445955884545689	0 14 18 30 108 134 140 168 200 228 234 260 338 350 354 368	414696766218
SPT(16)	2574446618798408873	0 26 30 38 44 56 60 96 98 134 138 150 156 164 168 194	1077610629402
STPT(10)	2574446854152748577	0 2 30 32 60 62 90 92 120 122	1312964969106
STPT(10)	2574446922069336071	0 2 6 8 18 20 30 32 36 38	1380881556600