Prime p₀= 781027070996741249 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 16 2 82 2 124 2 22 2 46 2 (?)
a_n: 0 2 30 32 48 50 132 134 258 260 282 284 330 332
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: 332
Found by: [SG]steini
db: batch=73, k=14, 28 16 82 124 22 46

STPT(12)	781025974744582199	0 2 12 14 42 44 48 50 78 80 90 92	-1096252159050
STPT(10)	781026166179542147	0 2 42 44 72 74 102 104 144 146	-904817199102
STPT(10)	781026287471684921	0 2 6 8 18 20 30 32 36 38	-783525056328
STPT(10)	781026388552684847	0 2 60 62 72 74 84 86 144 146	-682444056402
SPT(16)	781026390928420339	0 28 48 58 114 120 124 174 184 234 238 244 300 310 330 358	-680068320910
STPT(10)	781026435692471201	0 2 36 38 78 80 120 122 156 158	-635304270048
SPT(16)	781027307047597669	0 22 42 54 82 90 108 142 300 334 352 360 388 400 420 442	236050856420
STPT(10)	781027494244717199	0 2 18 20 30 32 42 44 60 62	423247975950
STPT(10)	781027512268097111	0 2 78 80 108 110 138 140 216 218	441271355862
SPT(16)	781028204997783641	0 30 42 62 92 120 122 162 176 216 218 246 276 296 308 338	1134001042392
SPT(16)	781028392391844929	0 44 50 78 90 92 140 194 198 252 300 302 314 342 348 392	1321395103680