Prime p₀= 3086367813627530141 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 40 2 16 2 10 2 28 2 28 2 (?)
a_n: 0 2 6 8 48 50 66 68 78 80 108 110 138 140
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: 140
Found by: JayPi
db: batch=83, k=14, 4 40 16 10 28 28

SPT(16)	3086365783517032427	0 14 54 56 116 132 182 206 210 234 284 300 360 362 402 416	-2030110497714
STPT(10)	3086366001554153567	0 2 60 62 72 74 84 86 144 146	-1812073376574
STPT(10)	3086366559797652977	0 2 24 26 42 44 60 62 84 86	-1253829877164
SPT(16)	3086367331555087357	0 10 16 24 30 40 66 82 84 100 126 136 142 150 156 166	-482072442784
SPT(16)	3086367430849846463	0 14 38 48 50 56 68 104 180 216 228 234 236 246 270 284	-382777683678
SPT(16)	3086367648718253797	0 16 30 46 76 106 112 132 214 234 240 270 300 316 330 346	-164909276344
SPT(16)	3086367892685221933	0 10 24 34 90 120 144 210 214 280 304 334 390 400 414 424	79057691792
SPT(16)	3086368079206165913	0 8 56 66 78 150 158 180 206 228 236 308 320 330 378 386	265578635772
SPT(16)	3086368167352690237	0 12 90 114 142 154 162 196 210 244 252 264 292 316 394 406	353725160096
TPT(14)	3086368558782303929	0 2 30 32 78 80 138 140 168 170 180 182 210 212	745154773788
STPT(10)	3086368846716098789	0 2 18 20 30 32 42 44 60 62	1033088568648