Prime p₀= 1298022015189593717 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 10 2 10 2 28 2 88 2 34 2 (?)
a_n: 0 2 60 62 72 74 84 86 114 116 204 206 240 242
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: 242
Found by: Cruncher Pete
db: batch=77, k=14, 58 10 10 28 88 34

STPT(10)	1298021026712598647	0 2 30 32 42 44 54 56 84 86	-988476995070
STPT(10)	1298021053768530071	0 2 30 32 78 80 126 128 156 158	-961421063646
SPT(16)	1298021075617789297	0 34 42 46 64 76 90 120 136 166 180 192 210 214 222 256	-939571804420
SPT(16)	1298021266511812093	0 28 30 118 168 184 220 226 228 234 270 286 336 424 426 454	-748677781624
STPT(10)	1298021311785723911	0 2 126 128 138 140 150 152 276 278	-703403869806
STPT(10)	1298021962669148411	0 2 30 32 60 62 90 92 120 122	-52520445306
SPT(16)	1298022399318656881	0 16 22 36 46 60 78 90 268 280 298 312 322 336 342 358	384129063164
STPT(10)	1298022422880025991	0 2 36 38 78 80 120 122 156 158	407690432274
STPT(10)	1298022569337334661	0 2 6 8 18 20 30 32 36 38	554147740944
STPT(10)	1298022831190912031	0 2 6 8 18 20 30 32 36 38	816001318314
SPT(16)	1298022838945460011	0 82 112 118 160 192 196 202 216 222 226 258 300 306 336 418	823755866294