Prime p₀= 1314714943052550161 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 58 2 22 2 28 2 64 2 10 2 (?)
a_n: 0 2 66 68 126 128 150 152 180 182 246 248 258 260
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: 260
Found by: gemini8
db: batch=77, k=14, 64 58 22 28 64 10

SPT(16)	1314714077460564371	0 12 30 42 90 138 192 210 218 236 290 338 386 398 416 428	-865591985790
STPT(10)	1314714114110298929	0 2 18 20 30 32 42 44 60 62	-828942251232
SPT(16)	1314714426444343933	0 4 40 66 94 100 126 156 208 238 264 270 298 324 360 364	-516608206228
STPT(10)	1314714805593628469	0 2 18 20 30 32 42 44 60 62	-137458921692
SPT(16)	1314714809379125597	0 6 36 44 56 86 122 146 150 174 210 240 252 260 290 296	-133673424564
STPT(12)	1314714928375393451	0 2 18 20 30 32 156 158 168 170 186 188	-14677156710
SPT(18)	1314715225823841089	0 2 24 48 62 84 108 122 150 212 240 254 278 300 314 338 360 362	282771290928
SPT(16)	1314715588658828911	0 16 48 66 70 90 150 168 178 196 256 276 280 298 330 346	645606278750
STPT(10)	1314715620719446109	0 2 132 134 150 152 168 170 300 302	677666895948
STPT(10)	1314715899875171147	0 2 54 56 72 74 90 92 144 146	956822620986
TPT(16)	1314716166144253427	0 2 42 44 144 146 240 242 282 284 294 296 450 452 492 494	1223091703266