Prime p₀= 2286739796331414101 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 76 2 28 2 16 2 10 2 106 2 (?)
a_n: 0 2 60 62 138 140 168 170 186 188 198 200 306 308
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: 308
Found by: Orange Kid
db: batch=81, k=14, 58 76 28 16 10 106

SPT(16)	2286738370360626197	0 12 14 26 66 72 92 110 126 144 164 170 210 222 224 236	-1425970787904
STPT(10)	2286738441113577419	0 2 42 44 90 92 138 140 180 182	-1355217836682
SPT(16)	2286738819958777999	0 34 40 100 132 184 240 262 282 304 360 412 444 504 510 544	-976372636102
STPT(10)	2286738977069791817	0 2 60 62 72 74 84 86 144 146	-819261622284
SPT(16)	2286739218273100973	0 26 44 54 78 96 126 144 170 188 218 236 260 270 288 314	-578058313128
STPT(10)	2286739504798760621	0 2 36 38 78 80 120 122 156 158	-291532653480
TPT(14)	2286739819886184779	0 2 30 32 138 140 240 242 312 314 420 422 468 470	23554770678
TPT(14)	2286739947615687827	0 2 72 74 102 104 132 134 222 224 312 314 324 326	151284273726
TPT(14)	2286740130208918931	0 2 108 110 156 158 378 380 420 422 450 452 486 488	333877504830
SPT(16)	2286740237767928473	0 6 18 40 76 84 124 150 244 270 310 318 354 376 388 394	441436514372
STPT(10)	2286740402141398031	0 2 6 8 48 50 90 92 96 98	605809983930