Prime p₀= 2037691977546657317 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 10 2 58 2 16 2 40 2 64 2 (?)
a_n: 0 2 42 44 54 56 114 116 132 134 174 176 240 242
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: 242
Found by: Landjunge
db: batch=80, k=14, 40 10 58 16 40 64

SPT(16)	2037688900137266401	0 12 16 22 28 78 102 112 156 166 190 240 246 252 256 268	-3077409390916
TPT(14)	2037689209039741247	0 2 12 14 42 44 84 86 210 212 222 224 282 284	-2768506916070
SPT(16)	2037689217674884271	0 18 60 68 86 102 180 212 336 368 446 462 480 488 530 548	-2759871773046
STPT(10)	2037690192565434917	0 2 42 44 72 74 102 104 144 146	-1784981222400
SPT(16)	2037691401589689061	0 88 102 150 216 220 228 238 240 250 258 262 328 376 390 478	-575956968256
SPT(16)	2037691907716078651	0 10 22 30 42 66 70 88 90 108 112 136 148 156 168 178	-69830578666
STPT(10)	2037692141639972117	0 2 24 26 42 44 60 62 84 86	164093314800
STPT(10)	2037692304439655621	0 2 6 8 18 20 30 32 36 38	326892998304
SPT(16)	2037692336467701061	0 12 66 78 108 156 186 196 222 232 262 310 340 352 406 418	358921043744
SPT(16)	2037692513150819663	0 20 54 68 80 120 134 246 248 360 374 414 426 440 474 494	535604162346
STPT(10)	2037693406933654367	0 2 60 62 72 74 84 86 144 146	1429386997050