Prime p₀= 1316415723491508791 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 58 2 88 2 4 2 28 2 10 2 (?)
a_n: 0 2 30 32 90 92 180 182 186 188 216 218 228 230
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: 230
Found by: [AF>Libristes] Elorak
db: batch=77, k=14, 28 58 88 4 28 10

STPT(10)	1316414814483831287	0 2 30 32 42 44 54 56 84 86	-909007677504
SPT(16)	1316414821874112707	0 54 60 90 104 152 174 182 234 242 264 312 326 356 362 416	-901617396084
SPT(18)	1316415072956444099	0 30 38 78 80 90 140 150 210 290 350 360 410 420 422 462 470 500	-650535064692
SPT(16)	1316415230701305277	0 22 46 64 70 76 102 154 162 214 240 246 252 270 294 316	-492790203514
SPT(16)	1316415329933894017	0 42 64 84 130 132 136 142 204 210 214 216 262 282 304 346	-393557614774
STPT(10)	1316415471769882877	0 2 30 32 42 44 54 56 84 86	-251721625914
STPT(10)	1316416794723116291	0 2 6 8 18 20 30 32 36 38	1071231607500
STPT(10)	1316416831230775667	0 2 30 32 42 44 54 56 84 86	1107739266876
STPT(10)	1316417126841439949	0 2 18 20 30 32 42 44 60 62	1403349931158
SPT(16)	1316417164366548113	0 6 24 90 108 116 126 156 158 188 198 206 224 290 308 314	1440875039322
STPT(10)	1316417560006764947	0 2 30 32 42 44 54 56 84 86	1836515256156