Prime p₀= 3008710571998486499 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 58 2 34 2 82 2 34 2 130 2 (?)
a_n: 0 2 42 44 102 104 138 140 222 224 258 260 390 392
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: [SG-2W]Kurzer
db: batch=82, k=14, 40 58 34 82 34 130

SPT(16)	3008710093938421123	0 18 28 30 70 94 108 124 144 160 174 198 238 240 250 268	-478060065376
SPT(16)	3008710107572781103	0 16 30 34 100 120 126 148 246 268 274 294 360 364 378 394	-464425705396
SPT(16)	3008710139262122551	0 58 78 88 198 202 226 252 286 312 336 340 450 460 480 538	-432736363948
SPT(16)	3008710233959938897	0 4 12 54 60 64 90 102 142 154 180 184 190 232 240 244	-338038547602
SPT(18)	3008710327823849303	0 6 14 26 56 110 146 156 186 224 254 264 300 354 384 396 404 410	-244174637196
STPT(10)	3008710488622022837	0 2 72 74 102 104 132 134 204 206	-83376463662
STPT(10)	3008710711958769029	0 2 42 44 60 62 78 80 120 122	139960282530
STPT(10)	3008710932404312711	0 2 36 38 78 80 120 122 156 158	360405826212
STPT(10)	3008711002873441037	0 2 30 32 42 44 54 56 84 86	430874954538
STPT(10)	3008711379278829281	0 2 36 38 78 80 120 122 156 158	807280342782
STPT(10)	3008711508397795001	0 2 6 8 48 50 90 92 96 98	936399308502