Prime p₀= 816554774796762887 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 16 2 10 2 28 2 10 2 46 2 (?)
a_n: 0 2 12 14 30 32 42 44 72 74 84 86 132 134
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: 134
Found by: [SG]FX
db: batch=73, k=14, 10 16 10 28 10 46

SPT(16)	816553542146406731	0 20 36 60 66 98 102 116 132 146 150 182 188 212 228 248	-1232650356156
SPT(16)	816553772105621227	0 54 84 96 174 186 192 196 240 244 250 262 340 352 382 436	-1002691141660
SPT(20)	816554049568059013	0 46 66 100 126 144 184 210 250 256 318 324 364 390 430 448 474 508 528 574	-725228703874
SPT(16)	816554099248648217	0 20 30 42 80 90 92 122 132 162 164 174 212 224 234 254	-675548114670
SPT(16)	816554363541618787	0 16 42 52 70 144 150 154 222 226 232 306 324 334 360 376	-411255144100
SPT(16)	816554564974679743	0 66 76 84 144 240 244 286 354 396 400 496 556 564 574 640	-209822083144
SPT(18)	816554812581798359	0 14 32 42 68 98 164 168 188 234 254 258 324 354 380 390 408 422	37785035472
SPT(16)	816554831448644273	0 6 56 86 110 116 168 228 278 338 390 396 420 450 500 506	56651881386
SPT(16)	816554901009070889	0 2 18 50 80 98 122 134 228 240 264 282 312 344 360 362	126212308002
SPT(16)	816555140384883701	0 6 32 60 92 146 162 180 182 200 216 270 302 330 356 362	365588120814
STPT(10)	816555283188351269	0 2 12 14 90 92 168 170 180 182	508391588382