Prime p₀= 960278324100859571 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 40 2 88 2 4 2 70 2 10 2 (?)
a_n: 0 2 78 80 120 122 210 212 216 218 288 290 300 302
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: 302
Found by: HenkM
db: batch=76, k=14, 76 40 88 4 70 10

STPT(10)	960277242363460919	0 2 18 20 30 32 42 44 60 62	-1081737398652
SPT(16)	960277302025655771	0 62 92 128 198 212 248 288 392 432 468 482 552 588 618 680	-1022075203800
SPT(16)	960277375672836803	0 26 38 50 74 84 138 140 204 206 260 270 294 306 318 344	-948428022768
TPT(14)	960277797795944279	0 2 42 44 78 80 150 152 210 212 222 224 288 290	-526304915292
SPT(16)	960277815234464789	0 14 32 62 74 122 140 150 164 174 192 240 252 282 300 314	-508866394782
STPT(12)	960277935593203649	0 2 30 32 42 44 90 92 102 104 132 134	-388507655922
SPT(16)	960278531522504611	0 6 48 58 60 96 106 138 148 180 190 226 228 238 280 286	207421645040
SPT(16)	960279168339642841	0 6 22 30 40 78 106 118 120 132 160 198 208 216 232 238	844238783270
STPT(10)	960279351441398081	0 2 30 32 60 62 90 92 120 122	1027340538510
TPT(14)	960279911388233627	0 2 42 44 90 92 120 122 144 146 162 164 270 272	1587287374056
STPT(10)	960279963892896629	0 2 12 14 90 92 168 170 180 182	1639792037058