Prime p₀= 4276920268548477929 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 46 2 82 2 46 2 28 2 10 2 (?)
a_n: 0 2 30 32 78 80 162 164 210 212 240 242 252 254
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: 254
Found by: Stony666
db: batch=85, k=14, 28 46 82 46 28 10

SPT(16)	4276919012337144091	0 22 28 36 90 102 130 142 216 228 256 268 322 330 336 358	-1256211333838
TPT(14)	4276919132891394851	0 2 36 38 78 80 138 140 168 170 198 200 210 212	-1135657083078
STPT(10)	4276919149544572547	0 2 30 32 120 122 210 212 240 242	-1119003905382
SPT(16)	4276919289163063397	0 24 26 44 56 126 162 180 236 254 290 360 372 390 392 416	-979385414532
STPT(10)	4276919469080456459	0 2 48 50 60 62 72 74 120 122	-799468021470
SPT(16)	4276920024318683351	0 12 26 32 68 80 110 152 156 198 228 240 276 282 296 308	-244229794578
STPT(12)	4276920268548477929	0 2 30 32 78 80 162 164 210 212 240 242	0
SPT(16)	4276920362627403221	0 8 42 152 170 180 198 206 252 260 278 288 306 416 450 458	94078925292
TPT(14)	4276920473775362321	0 2 60 62 96 98 126 128 150 152 210 212 228 230	205226884392
SPT(16)	4276920987122255011	0 12 18 30 88 96 102 112 156 166 172 180 238 250 256 268	718573777082
SPT(16)	4276921096068841921	0 10 22 28 46 70 72 100 108 136 138 162 180 186 198 208	827520363992