Prime p₀= 1294098037837206731 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 100 2 10 2 58 2 166 2 10 2 (?)
a_n: 0 2 6 8 108 110 120 122 180 182 348 350 360 362
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: Cruncher Pete
db: batch=77, k=14, 4 100 10 58 166 10

TPT(14)	1294096392570499541	0 2 6 8 18 20 78 80 90 92 126 128 168 170	-1645266707190
SPT(16)	1294096578872839319	0 44 50 54 68 140 174 204 278 308 342 414 428 432 438 482	-1458964367412
SPT(16)	1294096765923680863	0 6 46 58 60 100 118 126 130 138 156 196 198 210 250 256	-1271913525868
SPT(16)	1294097245744073941	0 22 30 36 42 46 48 70 78 100 102 106 112 118 126 148	-792093132790
STPT(10)	1294097245785811079	0 2 18 20 30 32 42 44 60 62	-792051395652
SPT(16)	1294097806445532139	0 34 42 64 84 88 94 108 214 228 234 238 258 280 288 322	-231391674592
STPT(10)	1294098285084833741	0 2 78 80 168 170 258 260 336 338	247247627010
SPT(16)	1294098334906254827	0 14 42 50 56 104 182 210 236 264 342 390 396 404 432 446	297069048096
STPT(10)	1294098402315096407	0 2 30 32 42 44 54 56 84 86	364477889676
STPT(10)	1294098508727691809	0 2 18 20 30 32 42 44 60 62	470890485078
STPT(10)	1294098900584162999	0 2 18 20 30 32 42 44 60 62	862746956268