Prime p₀= 1246841076133822781 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 28 2 16 2 82 2 46 2 46 2 (?)
a_n: 0 2 78 80 108 110 126 128 210 212 258 260 306 308
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: Cruncher Pete
db: batch=77, k=14, 76 28 16 82 46 46

SPT(16)	1246839974245469039	0 14 30 38 60 80 98 168 200 270 288 308 330 338 354 368	-1101888353742
STPT(10)	1246840399155808151	0 2 30 32 60 62 90 92 120 122	-676978014630
SPT(16)	1246840688318958973	0 4 18 34 64 94 108 144 160 196 210 240 270 286 300 304	-387814863808
STPT(10)	1246840690238639729	0 2 48 50 60 62 72 74 120 122	-385895183052
STPT(10)	1246841066884583699	0 2 12 14 90 92 168 170 180 182	-9249239082
TPT(14)	1246841066884583699	0 2 12 14 90 92 168 170 180 182 222 224 300 302	-9249239082
STPT(10)	1246841324518960097	0 2 42 44 72 74 102 104 144 146	248385137316
SPT(16)	1246841469186429041	0 2 48 66 78 92 98 116 132 150 156 170 182 200 246 248	393052606260
STPT(10)	1246841695577809151	0 2 6 8 18 20 30 32 36 38	619443986370
STPT(10)	1246841863971859577	0 2 90 92 102 104 114 116 204 206	787838036796
SPT(16)	1246842710501212081	0 22 36 52 66 76 132 160 252 280 336 346 360 376 390 412	1634367389300