Prime p₀= 813772317672675869 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 136 2 58 2 22 2 34 2 40 2 40 2 (?)
a_n: 0 2 138 140 198 200 222 224 258 260 300 302 342 344
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: 344
Found by: [SG]FX
db: batch=73, k=14, 136 58 22 34 40 40

SPT(13)	813771706708262849	0 18 24 60 78 108 144 180 210 228 264 270 288	-610964413020
SPT(16)	813771711957151201	0 18 28 48 102 112 150 160 168 178 216 226 280 300 310 328	-605715524668
SPT(16)	813771724228958921	0 6 32 48 72 86 132 150 188 206 252 266 290 306 332 338	-593443716948
STPT(10)	813771977398176827	0 2 30 32 60 62 90 92 120 122	-340274499042
SPT(16)	813772103098981799	0 38 50 68 92 108 164 194 288 318 374 390 414 432 444 482	-214573694070
STPT(10)	813772210214859947	0 2 42 44 102 104 162 164 204 206	-107457815922
SPT(16)	813772631814129293	0 54 78 96 146 168 176 186 218 228 236 258 308 326 350 404	314141453424
SPT(16)	813772878221167979	0 24 38 60 72 78 98 102 140 144 164 170 182 204 218 242	560548492110
STPT(10)	813773026318108847	0 2 84 86 132 134 180 182 264 266	708645432978
STPT(10)	813773041977412301	0 2 36 38 78 80 120 122 156 158	724304736432
TPT(14)	813773365352007341	0 2 30 32 78 80 108 110 156 158 180 182 210 212	1047679331472