Prime p₀= 2678419696289637281 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 100 2 34 2 40 2 10 2 4 2 (?)
a_n: 0 2 18 20 120 122 156 158 198 200 210 212 216 218
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: 218
Found by: [SG-2W]Kurzer
db: batch=82, k=14, 16 100 34 40 10 4

STPT(10)	2678418292556836757	0 2 30 32 72 74 114 116 144 146	-1403732800524
SPT(16)	2678418551117356813	0 16 24 124 126 138 178 264 280 366 406 418 420 520 528 544	-1145172280468
STPT(10)	2678419077782040137	0 2 30 32 42 44 54 56 84 86	-618507597144
STPT(10)	2678419230691292351	0 2 6 8 48 50 90 92 96 98	-465598344930
STPT(10)	2678419413891090011	0 2 6 8 18 20 30 32 36 38	-282398547270
SPT(16)	2678419424680650683	0 18 48 68 74 110 114 140 174 200 204 240 246 266 296 314	-271608986598
TPT(14)	2678419990866582449	0 2 12 14 60 62 132 134 198 200 210 212 300 302	294576945168
SPT(16)	2678420245427631791	0 20 48 50 60 78 86 98 120 132 140 158 168 170 198 218	549137994510
SPT(16)	2678420405748986993	0 6 26 44 66 80 96 156 188 248 264 278 300 318 338 344	709459349712
SPT(16)	2678420966108497879	0 12 34 42 52 58 84 114 118 148 174 180 190 198 220 232	1269818860598
SPT(16)	2678421113291660677	0 12 22 24 52 72 90 124 150 184 202 222 250 252 262 274	1417002023396