Prime p₀= 797309604678445721 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 4 2 82 2 4 2 58 2 10 2 (?)
a_n: 0 2 30 32 36 38 120 122 126 128 186 188 198 200
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: 200
Found by: [SG-2W]Kurzer
db: batch=73, k=14, 28 4 82 4 58 10

TPT(14)	797308382039271017	0 2 24 26 144 146 180 182 192 194 222 224 264 266	-1222639174704
SPT(16)	797308616289913513	0 10 58 60 76 90 100 108 136 144 154 168 184 186 234 244	-988388532208
STPT(10)	797308867984306157	0 2 30 32 42 44 54 56 84 86	-736694139564
SPT(16)	797309106440714909	0 2 48 60 74 104 140 174 308 342 378 408 422 434 480 482	-498237730812
TPT(14)	797309170815564257	0 2 30 32 90 92 102 104 144 146 180 182 210 212	-433862881464
SPT(16)	797309576316451273	0 6 34 40 64 78 96 106 108 118 136 150 174 180 208 214	-28361994448
STPT(10)	797310018912908297	0 2 24 26 42 44 60 62 84 86	414234462576
SPT(16)	797310206748229969	0 40 88 112 114 144 148 204 208 264 268 298 300 324 372 412	602069784248
STPT(10)	797310583439107889	0 2 48 50 90 92 132 134 180 182	978760662168
SPT(16)	797310773120883011	0 18 48 68 90 126 128 158 210 240 242 278 300 320 350 368	1168442437290
STPT(10)	797310937477508549	0 2 18 20 30 32 42 44 60 62	1332799062828