Prime p₀= 1282483164438625211 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 46 2 130 2 28 2 34 2 82 2 (?)
a_n: 0 2 60 62 108 110 240 242 270 272 306 308 390 392
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: 392
Found by: Cruncher Pete
db: batch=77, k=14, 58 46 130 28 34 82

SPT(16)	1282482471530537861	0 48 68 72 138 140 150 162 308 320 330 332 398 402 422 470	-692908087350
STPT(10)	1282482607811443931	0 2 6 8 48 50 90 92 96 98	-556627181280
SPT(16)	1282482685987914953	0 14 44 48 78 98 120 128 216 224 246 266 296 300 330 344	-478450710258
SPT(16)	1282482712523368297	0 22 42 54 82 90 112 120 166 174 196 204 232 244 264 286	-451915256914
STPT(10)	1282482871618051811	0 2 36 38 78 80 120 122 156 158	-292820573400
SPT(16)	1282482932671177163	0 86 98 164 198 210 224 264 290 330 344 356 390 456 468 554	-231767448048
TPT(14)	1282483329939000197	0 2 54 56 72 74 84 86 114 116 240 242 282 284	165500374986
SPT(16)	1282483492881124601	0 42 78 86 90 92 152 158 240 246 306 308 312 320 356 398	328442499390
STPT(10)	1282484261174644667	0 2 12 14 42 44 72 74 84 86	1096736019456
SPT(16)	1282484320911766019	0 20 24 78 138 150 168 194 204 230 248 260 320 374 378 398	1156473140808
SPT(16)	1282484569457161003	0 40 48 76 138 150 168 196 258 286 304 316 378 406 414 454	1405018535792