Prime p₀= 2016499308204658619 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 22 2 58 2 4 2 70 2 10 2 (?)
a_n: 0 2 18 20 42 44 102 104 108 110 180 182 192 194
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: 194
Found by: vaughan
db: batch=80, k=14, 16 22 58 4 70 10

SPT(16)	2016498403248191623	0 18 24 48 60 76 96 126 178 208 228 244 256 280 286 304	-904956466996
TPT(14)	2016498413348122061	0 2 66 68 180 182 210 212 276 278 360 362 378 380	-894856536558
SPT(16)	2016498427704126979	0 12 18 22 40 54 90 132 160 202 238 252 270 274 280 292	-880500531640
STPT(10)	2016498509510609819	0 2 30 32 60 62 90 92 120 122	-798694048800
SPT(16)	2016498642807897733	0 18 24 28 64 70 84 94 210 220 234 240 276 280 286 304	-665396760886
SPT(16)	2016499016968795393	0 4 30 46 48 60 88 90 124 126 154 166 168 184 210 214	-291235863226
STPT(10)	2016499399021029227	0 2 30 32 42 44 54 56 84 86	90816370608
SPT(16)	2016499628945326573	0 10 34 48 60 70 114 130 138 154 198 208 220 234 258 268	320740667954
STPT(10)	2016499669730154797	0 2 24 26 42 44 60 62 84 86	361525496178
SPT(16)	2016499912979312723	0 36 74 78 128 134 140 158 186 204 210 216 266 270 308 344	604774654104
STPT(10)	2016500065217228951	0 2 6 8 48 50 90 92 96 98	757012570332