Prime p₀= 2556600617525394071 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 124 2 28 2 10 2 58 2 10 2 (?)
a_n: 0 2 60 62 186 188 216 218 228 230 288 290 300 302
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: 302
Found by: Penguin
db: batch=82, k=14, 58 124 28 10 58 10

SPT(16)	2556598576749299591	0 26 36 38 66 138 150 158 168 176 188 260 288 290 300 326	-2040776094480
TPT(14)	2556598706966777327	0 2 30 32 162 164 180 182 204 206 294 296 324 326	-1910558616744
SPT(16)	2556598903095610631	0 12 62 90 126 140 152 170 198 216 228 242 278 306 356 368	-1714429783440
STPT(10)	2556599868194392817	0 2 24 26 42 44 60 62 84 86	-749331001254
SPT(16)	2556600152158390763	0 8 14 18 54 78 90 200 204 314 326 350 386 390 396 404	-465367003308
STPT(10)	2556600199836185939	0 2 42 44 60 62 78 80 120 122	-417689208132
SPT(16)	2556600793051931809	0 42 52 54 82 124 162 208 264 310 348 390 418 420 430 472	175526537738
STPT(10)	2556600976724087747	0 2 24 26 42 44 60 62 84 86	359198693676
STPT(10)	2556601070213078561	0 2 30 32 78 80 126 128 156 158	452687684490
SPT(16)	2556601166582115571	0 6 48 102 106 118 156 190 198 232 270 282 286 340 382 388	549056721500
STPT(10)	2556601398735564977	0 2 30 32 42 44 54 56 84 86	781210170906