Prime p₀= 2045598657130020269 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 70 2 28 2 34 2 28 2 58 2 (?)
a_n: 0 2 30 32 102 104 132 134 168 170 198 200 258 260
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: 260
Found by: Landjunge
db: batch=80, k=14, 28 70 28 34 28 58

SPT(16)	2045597140038330899	0 14 18 30 62 80 104 114 158 168 192 210 242 254 258 272	-1517091689370
SPT(16)	2045597502085122529	0 12 18 40 48 52 102 108 112 118 168 172 180 202 208 220	-1155044897740
STPT(10)	2045597664507625367	0 2 60 62 72 74 84 86 144 146	-992622394902
TPT(14)	2045598153555619757	0 2 12 14 54 56 90 92 132 134 162 164 204 206	-503574400512
SPT(16)	2045598369214464143	0 6 48 50 66 84 98 114 140 156 170 188 204 206 248 254	-287915556126
SPT(16)	2045598456939866249	0 32 54 84 102 122 128 180 182 234 240 260 278 308 330 362	-200190154020
SPT(16)	2045598940592213077	0 4 24 40 42 66 82 96 100 114 130 154 156 172 192 196	283462192808
SPT(16)	2045598957521541101	0 8 18 30 38 42 72 80 198 206 236 240 248 260 270 278	300391520832
STPT(10)	2045599096498226411	0 2 6 8 18 20 30 32 36 38	439368206142
SPT(16)	2045599631105029609	0 4 18 30 58 64 100 154 264 318 354 360 388 400 414 418	973975009340
TPT(14)	2045599669770464711	0 2 36 38 120 122 138 140 168 170 246 248 288 290	1012640444442