Prime p₀= 1538011636608423731 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 76 2 130 2 166 2 10 2 28 2 (?)
a_n: 0 2 18 20 96 98 228 230 396 398 408 410 438 440
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: 440
Found by: crashtech
db: batch=78, k=14, 16 76 130 166 10 28

SPT(16)	1538010544663506203	0 20 26 36 38 90 108 140 174 206 224 276 278 288 294 314	-1091944917528
SPT(16)	1538010783072423307	0 42 60 76 112 162 174 186 190 202 214 264 300 316 334 376	-853536000424
STPT(10)	1538011263320737781	0 2 36 38 78 80 120 122 156 158	-373287685950
SPT(16)	1538011312764648109	0 10 24 58 64 82 94 112 120 138 150 168 174 208 222 232	-323843775622
SPT(16)	1538011502379997633	0 6 30 46 58 60 94 114 130 150 184 186 198 214 238 244	-134228426098
SPT(16)	1538011551924752783	0 30 48 120 126 156 168 186 240 258 270 300 306 378 396 426	-84683670948
STPT(10)	1538011691547867059	0 2 18 20 30 32 42 44 60 62	54939443328
STPT(10)	1538011960339006697	0 2 30 32 42 44 54 56 84 86	323730582966
TPT(14)	1538012384617792709	0 2 132 134 150 152 162 164 288 290 300 302 372 374	748009368978
SPT(16)	1538012460241370947	0 4 10 52 54 70 72 82 114 124 126 142 144 186 192 196	823632947216
STPT(10)	1538012842969624907	0 2 30 32 42 44 54 56 84 86	1206361201176