Prime p₀= 2639256609212734241 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 10 2 34 2 40 2 118 2 16 2 (?)
a_n: 0 2 78 80 90 92 126 128 168 170 288 290 306 308
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: 308
Found by: paulteo
db: batch=82, k=14, 76 10 34 40 118 16

SPT(16)	2639255374852956227	0 12 44 56 92 140 156 176 180 200 216 264 300 312 344 356	-1234359778014
STPT(10)	2639255682439563329	0 2 18 20 30 32 42 44 60 62	-926773170912
SPT(16)	2639255755096640923	0 6 66 106 154 174 178 220 234 276 280 300 348 388 448 454	-854116093318
STPT(10)	2639255760384124559	0 2 18 20 30 32 42 44 60 62	-848828609682
STPT(10)	2639255852695101707	0 2 12 14 72 74 132 134 144 146	-756517632534
STPT(10)	2639256370062465911	0 2 6 8 18 20 30 32 36 38	-239150268330
SPT(16)	2639256929264040311	0 48 62 72 116 146 150 228 230 308 312 342 386 396 410 458	320051306070
STPT(10)	2639257269218589989	0 2 12 14 30 32 48 50 60 62	660005855748
SPT(16)	2639257322837555561	0 36 42 72 92 96 110 182 240 312 326 330 350 380 386 422	713624821320
STPT(10)	2639257452543918551	0 2 36 38 78 80 120 122 156 158	843331184310
TPT(14)	2639257877038834211	0 2 30 32 96 98 210 212 240 242 318 320 336 338	1267826099970