Prime p₀= 2999255258125459787 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 58 2 34 2 82 2 4 2 22 2 (?)
a_n: 0 2 54 56 114 116 150 152 234 236 240 242 264 266
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: 266
Found by: Orange Kid
db: batch=82, k=14, 52 58 34 82 4 22

SPT(16)	2999254597629020221	0 10 12 52 66 102 106 130 228 252 256 292 306 346 348 358	-660496439566
SPT(16)	2999254655945894771	0 18 80 96 110 150 162 192 236 266 278 318 332 348 410 428	-602179565016
SPT(16)	2999254782703498673	0 18 30 78 138 168 170 194 204 228 230 260 320 368 380 398	-475421961114
TPT(14)	2999254811779788929	0 2 48 50 78 80 162 164 180 182 210 212 288 290	-446345670858
SPT(16)	2999255095711991569	0 10 12 48 52 60 70 82 90 102 112 120 124 160 162 172	-162413468218
SPT(16)	2999255191711972969	0 24 34 42 124 178 210 250 312 352 384 438 520 528 538 562	-66413486818
STPT(10)	2999255537327048117	0 2 30 32 42 44 54 56 84 86	279201588330
SPT(16)	2999255704919021453	0 24 96 104 138 140 146 170 174 198 204 206 240 248 320 344	446793561666
SPT(16)	2999255864472103157	0 26 54 56 102 164 180 192 224 236 252 314 360 362 390 416	606346643370
SPT(16)	2999256090565852823	0 14 44 80 84 104 144 170 228 254 294 314 318 354 384 398	832440393036
STPT(10)	2999256091376571779	0 2 18 20 30 32 42 44 60 62	833251111992