Prime p₀= 1025713414536942827 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 130 2 58 2 16 2 22 2 16 2 46 2 (?)
a_n: 0 2 132 134 192 194 210 212 234 236 252 254 300 302
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: Spectrum
db: batch=76, k=14, 130 58 16 22 16 46

STPT(10)	1025711586904659047	0 2 30 32 42 44 54 56 84 86	-1827632283780
STPT(10)	1025711636933913899	0 2 12 14 30 32 48 50 60 62	-1777603028928
SPT(16)	1025711673758078627	0 14 24 102 126 132 146 152 264 270 284 290 314 392 402 416	-1740778864200
SPT(16)	1025712556721054171	0 50 72 78 138 180 198 210 230 242 260 302 362 368 390 440	-857815888656
STPT(10)	1025712994826805821	0 2 6 8 48 50 90 92 96 98	-419710137006
STPT(10)	1025713022850342257	0 2 30 32 72 74 114 116 144 146	-391686600570
SPT(16)	1025713508640060091	0 10 12 36 66 82 112 148 150 186 216 232 262 286 288 298	94103117264
STPT(10)	1025713574697541781	0 2 6 8 18 20 30 32 36 38	160160598954
SPT(16)	1025713683390417809	0 8 54 78 98 134 188 194 198 204 258 294 314 338 384 392	268853474982
STPT(10)	1025714069705510957	0 2 30 32 72 74 114 116 144 146	655168568130
SPT(16)	1025714156807742331	0 70 72 88 118 130 132 138 160 166 168 180 210 226 228 298	742270799504