Prime p₀= 2836963968719978309 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 58 2 184 2 22 2 28 2 34 2 (?)
a_n: 0 2 42 44 102 104 288 290 312 314 342 344 378 380
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: 380
Found by: Roadranner
db: batch=82, k=14, 40 58 184 22 28 34

SPT(16)	2836962117320380529	0 30 42 74 84 98 120 132 140 152 174 188 198 230 242 272	-1851399597780
SPT(16)	2836962337407325327	0 22 36 46 70 90 106 120 172 186 202 222 246 256 270 292	-1631312652982
TPT(14)	2836962556116643697	0 2 12 14 84 86 150 152 162 164 240 242 252 254	-1412603334612
STPT(10)	2836963320318810437	0 2 42 44 72 74 102 104 144 146	-648401167872
SPT(16)	2836963639560679259	0 8 14 50 60 74 78 108 170 200 204 218 228 264 270 278	-329159299050
SPT(16)	2836963782568831247	0 44 56 72 92 146 150 252 254 356 360 414 434 450 462 506	-186151147062
SPT(16)	2836964277357209633	0 8 14 20 36 54 74 110 204 240 260 278 294 300 306 314	308637231324
SPT(16)	2836964577400361137	0 30 36 66 94 100 112 126 130 144 156 162 190 220 226 256	608680382828
SPT(16)	2836964641937606749	0 10 34 52 64 70 84 174 220 310 324 330 342 360 384 394	673217628440
STPT(12)	2836965439234105547	0 2 12 14 42 44 60 62 90 92 102 104	1470514127238
SPT(16)	2836965600484225073	0 8 26 48 66 96 156 164 180 188 248 278 296 318 336 344	1631764246764