Prime p₀= 1266457486178234489 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 106 2 88 2 10 2 94 2 10 2 (?)
a_n: 0 2 42 44 150 152 240 242 252 254 348 350 360 362
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: 362
Found by: Megacruncher
db: batch=77, k=14, 40 106 88 10 94 10

SPT(16)	1266456653413186369	0 40 60 70 78 102 138 144 148 154 190 214 222 232 252 292	-832765048120
STPT(10)	1266456661715017481	0 2 36 38 78 80 120 122 156 158	-824463217008
TPT(14)	1266456846544462751	0 2 120 122 168 170 276 278 318 320 330 332 336 338	-639633771738
TPT(14)	1266457002755034581	0 2 30 32 36 38 78 80 108 110 126 128 138 140	-483423199908
STPT(10)	1266457464983773859	0 2 18 20 30 32 42 44 60 62	-21194460630
SPT(16)	1266457474619922413	0 14 20 48 50 66 96 110 204 218 248 264 266 294 300 314	-11558312076
STPT(10)	1266457647260966117	0 2 60 62 72 74 84 86 144 146	161082731628
SPT(16)	1266457996394941739	0 12 60 68 152 182 188 210 230 252 258 288 372 380 428 440	510216707250
SPT(16)	1266458474422878389	0 24 80 90 122 164 170 210 212 252 258 300 332 342 398 422	988244643900
SPT(16)	1266458499195208463	0 8 36 44 78 128 144 146 198 200 216 266 300 308 336 344	1013016973974
SPT(16)	1266458596546201199	0 12 18 42 78 120 140 144 278 282 302 344 380 404 410 422	1110367966710