Prime p₀= 2044135857939262931 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 130 2 46 2 10 2 58 2 10 2 (?)
a_n: 0 2 6 8 138 140 186 188 198 200 258 260 270 272
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: 272
Found by: Orange Kid
db: batch=80, k=14, 4 130 46 10 58 10

SPT(16)	2044134498555601741	0 16 58 76 112 132 150 178 210 238 256 276 312 330 372 388	-1359383661190
TPT(14)	2044134529062766199	0 2 12 14 48 50 78 80 90 92 180 182 210 212	-1328876496732
SPT(13)	2044134589446620381	0 12 36 42 90 96 126 156 162 210 216 240 252	-1268492642550
STPT(10)	2044134981396905867	0 2 30 32 42 44 54 56 84 86	-876542357064
SPT(16)	2044135609281260731	0 36 46 48 126 130 132 136 162 166 168 172 250 252 262 298	-248658002200
SPT(16)	2044135722498177571	0 18 40 46 60 138 156 160 168 172 190 268 282 288 310 328	-135441085360
TPT(16)	2044135944133708751	0 2 18 20 60 62 198 200 216 218 300 302 306 308 408 410	86194445820
STPT(10)	2044135951022023679	0 2 42 44 60 62 78 80 120 122	93082760748
STPT(10)	2044137156048258839	0 2 72 74 120 122 168 170 240 242	1298108995908
SPT(16)	2044137895098830651	0 8 32 92 98 128 150 162 248 260 282 312 318 378 402 410	2037159567720
SPT(16)	2044137982750932001	0 30 52 72 120 138 156 168 190 202 220 238 286 306 328 358	2124811669070