Prime p₀= 2799144812862214979 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 106 2 82 2 304 2 40 2 28 2 (?)
a_n: 0 2 30 32 138 140 222 224 528 530 570 572 600 602
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: JayPi
db: batch=82, k=14, 28 106 82 304 40 28

SPT(16)	2799144000085469233	0 10 18 46 108 120 130 138 238 246 256 268 330 358 366 376	-812776745746
STPT(10)	2799144226789058177	0 2 12 14 42 44 72 74 84 86	-586073156802
SPT(16)	2799144281715606491	0 6 56 72 98 170 182 192 206 216 228 300 326 342 392 398	-531146608488
SPT(16)	2799144472488558043	0 28 120 150 160 204 220 258 280 318 334 378 388 418 510 538	-340373656936
SPT(16)	2799144690253267963	0 34 40 46 54 76 118 124 210 216 258 280 288 294 300 334	-122608947016
TPT(14)	2799144812575515821	0 2 60 62 96 98 156 158 216 218 240 242 366 368	-286699158
SPT(16)	2799144884768462611	0 52 72 118 132 156 160 196 222 258 262 286 300 346 366 418	71906247632
TPT(14)	2799145213475580887	0 2 84 86 150 152 162 164 282 284 360 362 372 374	400613365908
SPT(16)	2799145294006179271	0 10 112 118 126 178 196 238 240 282 300 352 360 366 468 478	481143964292
STPT(10)	2799145344138516557	0 2 30 32 60 62 90 92 120 122	531276301578
SPT(16)	2799145417236482123	0 24 84 96 174 194 216 234 260 278 300 320 398 410 470 494	604374267144