Prime p₀= 862729757900502761 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 118 2 4 2 40 2 88 2 16 2 22 2 (?)
a_n: 0 2 120 122 126 128 168 170 258 260 276 278 300 302
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: [SG-2W]Kurzer
db: batch=73, k=14, 118 4 40 88 16 22

STPT(10)	862728795361144289	0 2 42 44 90 92 138 140 180 182	-962539358472
TPT(14)	862728929163483617	0 2 102 104 132 134 222 224 240 242 264 266 312 314	-828737019144
STPT(10)	862729077129907061	0 2 6 8 48 50 90 92 96 98	-680770595700
STPT(10)	862729374571365311	0 2 6 8 48 50 90 92 96 98	-383329137450
SPT(16)	862729493133754201	0 28 46 72 90 112 138 142 186 190 216 238 256 282 300 328	-264766748560
SPT(16)	862729678841063549	0 18 74 80 90 98 120 164 228 272 294 302 312 318 374 392	-79059439212
STPT(10)	862730172787782119	0 2 18 20 30 32 42 44 60 62	414887279358
SPT(16)	862730250969503269	0 34 42 52 72 94 112 150 184 222 240 262 282 292 300 334	493069000508
SPT(20)	862730552264944579	0 52 54 60 90 108 124 138 144 160 192 208 214 228 244 262 292 298 300 352	794364441818
TPT(14)	862730871258460481	0 2 6 8 156 158 366 368 378 380 396 398 648 650	1113357957720
SPT(16)	862730968240698457	0 6 40 46 64 130 162 180 196 214 246 312 330 336 370 376	1210340195696