Prime p₀= 2865140975152480559 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 130 2 4 2 22 2 136 2 286 2 10 2 (?)
a_n: 0 2 132 134 138 140 162 164 300 302 588 590 600 602
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: 602
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 130 4 22 136 286 10

STPT(10)	2865139759372422137	0 2 12 14 72 74 132 134 144 146	-1215780058422
STPT(10)	2865139787515882907	0 2 30 32 60 62 90 92 120 122	-1187636597652
SPT(16)	2865140065803118427	0 2 30 74 114 134 174 200 216 242 282 302 342 386 414 416	-909349362132
SPT(16)	2865140181512726101	0 46 70 78 90 96 112 130 168 186 202 208 220 228 252 298	-793639754458
STPT(10)	2865140334167126921	0 2 6 8 48 50 90 92 96 98	-640985353638
STPT(10)	2865140518872991661	0 2 30 32 78 80 126 128 156 158	-456279488898
STPT(10)	2865141114737070077	0 2 30 32 42 44 54 56 84 86	139584589518
STPT(10)	2865141810962512127	0 2 54 56 72 74 90 92 144 146	835810031568
SPT(16)	2865142929421543747	0 42 54 64 106 124 126 132 274 280 282 300 342 352 364 406	1954269063188
SPT(16)	2865143310109042847	0 30 66 150 152 174 176 180 206 210 212 234 236 320 356 386	2334956562288
SPT(16)	2865143329122852751	0 28 46 52 100 108 112 120 178 186 190 198 246 252 270 298	2353970372192