Prime p₀= 2029122517764163397 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 88 2 40 2 34 2 40 2 16 2 (?)
a_n: 0 2 42 44 132 134 174 176 210 212 252 254 270 272
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: 272
Found by: Landjunge
db: batch=80, k=14, 40 88 40 34 40 16

SPT(16)	2029121156345173663	0 10 24 48 58 174 210 216 328 334 370 486 496 520 534 544	-1361418989734
SPT(16)	2029121483802384701	0 8 20 36 38 48 78 122 126 170 200 210 212 228 240 248	-1033961778696
STPT(10)	2029121653886703161	0 2 36 38 78 80 120 122 156 158	-863877460236
SPT(16)	2029121741180682209	0 14 20 62 78 90 92 120 122 150 152 164 180 222 228 242	-776583481188
STPT(10)	2029121834432541377	0 2 60 62 72 74 84 86 144 146	-683331622020
STPT(10)	2029122033115093067	0 2 84 86 132 134 180 182 264 266	-484649070330
STPT(10)	2029122791512353767	0 2 24 26 42 44 60 62 84 86	273748190370
SPT(16)	2029122792619553731	0 60 126 132 156 162 168 172 216 220 226 232 256 262 328 388	274855390334
SPT(16)	2029122813800662589	0 8 14 38 44 50 72 92 150 170 192 198 204 228 234 242	296036499192
STPT(10)	2029122859772734511	0 2 36 38 78 80 120 122 156 158	342008571114
SPT(16)	2029123023340625941	0 16 18 36 78 106 126 210 226 310 330 358 400 418 420 436	505576462544