Prime p₀= 2129357612048068679 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 106 2 10 2 16 2 190 2 (?)
a_n: 0 2 30 32 60 62 168 170 180 182 198 200 390 392
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: 392
Found by: Orange Kid
db: batch=80, k=14, 28 28 106 10 16 190

SPT(16)	2129355984373274147	0 44 50 74 80 96 102 110 126 134 140 156 162 186 192 236	-1627674794532
SPT(16)	2129356040502847483	0 4 78 84 90 150 160 174 250 264 274 334 340 346 420 424	-1571545221196
SPT(16)	2129356086607728421	0 6 10 70 126 132 256 276 346 366 490 496 552 612 616 622	-1525440340258
SPT(16)	2129356495175198297	0 30 56 92 120 134 156 210 326 380 402 416 444 480 506 536	-1116872870382
SPT(16)	2129356723459211483	0 24 26 48 54 90 98 108 146 156 164 200 206 228 230 254	-888588857196
SPT(16)	2129357319295204451	0 8 38 96 120 140 146 176 192 222 228 248 272 330 360 368	-292752864228
STPT(10)	2129358160738084877	0 2 42 44 72 74 102 104 144 146	548690016198
STPT(10)	2129358238904076137	0 2 42 44 72 74 102 104 144 146	626856007458
STPT(10)	2129358293266314137	0 2 24 26 42 44 60 62 84 86	681218245458
SPT(16)	2129359351106580557	0 12 54 84 86 90 96 144 182 230 236 240 242 272 314 326	1739058511878
TPT(14)	2129359419211743461	0 2 66 68 150 152 156 158 306 308 408 410 420 422	1807163674782