Prime p₀= 1142946909128630657 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 16 2 142 2 64 2 70 2 (?)
a_n: 0 2 30 32 42 44 60 62 204 206 270 272 342 344
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: 344
Found by: Alnitak2019
db: batch=76, k=14, 28 10 16 142 64 70

STPT(10)	1142945094616025681	0 2 36 38 78 80 120 122 156 158	-1814512604976
SPT(16)	1142945437124126011	0 28 46 48 52 70 120 136 162 178 228 246 250 252 270 298	-1472004504646
SPT(16)	1142945934480819967	0 66 70 84 106 112 150 166 180 196 234 240 262 276 280 346	-974647810690
SPT(16)	1142946252019042439	0 20 42 44 78 90 92 104 198 210 212 224 258 260 282 302	-657109588218
SPT(16)	1142946634409084629	0 18 24 48 60 64 70 88 234 252 258 262 274 298 304 322	-274719546028
SPT(16)	1142946789156382981	0 30 42 88 108 112 138 198 220 280 306 310 330 376 388 418	-119972247676
STPT(10)	1142946947825757551	0 2 36 38 78 80 120 122 156 158	38697126894
SPT(16)	1142947008268907323	0 6 28 66 94 124 136 138 196 198 210 240 268 306 328 334	99140276666
SPT(16)	1142947607987213449	0 4 10 40 70 100 114 144 148 178 192 222 252 282 288 292	698858582792
TPT(14)	1142947646203288997	0 2 54 56 240 242 264 266 372 374 390 392 414 416	737074658340
STPT(10)	1142947982331075617	0 2 30 32 72 74 114 116 144 146	1073202444960