Prime p₀= 2375419861585790951 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 28 2 28 2 22 2 88 2 4 2 (?)
a_n: 0 2 66 68 96 98 126 128 150 152 240 242 246 248
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: 248
Found by: Landjunge
db: batch=81, k=14, 64 28 28 22 88 4

STPT(12)	2375419124715371939	0 2 12 14 72 74 78 80 138 140 150 152	-736870419012
SPT(16)	2375419167034108651	0 18 40 112 136 150 186 190 228 232 268 282 306 378 400 418	-694551682300
TPT(14)	2375419192755599537	0 2 30 32 54 56 84 86 120 122 150 152 222 224	-668830191414
STPT(10)	2375419829656647209	0 2 18 20 60 62 102 104 120 122	-31929143742
SPT(16)	2375419830539458013	0 26 50 54 56 78 146 150 164 168 236 258 260 264 288 314	-31046332938
SPT(16)	2375419843471577687	0 44 66 74 80 92 102 110 126 134 144 156 162 170 192 236	-18114213264
SPT(16)	2375419989767521973	0 44 68 96 108 138 156 170 174 188 206 236 248 276 300 344	128181731022
STPT(10)	2375420184073330391	0 2 6 8 48 50 90 92 96 98	322487539440
SPT(16)	2375420296434288211	0 12 76 82 136 148 160 162 166 168 180 192 246 252 316 328	434848497260
SPT(16)	2375420333551106473	0 16 66 136 190 196 216 238 276 298 318 324 378 448 498 514	471965315522
SPT(16)	2375420512140545957	0 2 24 26 44 50 62 80 96 114 126 132 150 152 174 176	650554755006