Prime p₀= 2361573937275946427 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 58 2 40 2 64 2 28 2 22 2 (?)
a_n: 0 2 12 14 72 74 114 116 180 182 210 212 234 236
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: 236
Found by: Landjunge
db: batch=81, k=14, 10 58 40 64 28 22

STPT(10)	2361571693883038337	0 2 30 32 42 44 54 56 84 86	-2243392908090
STPT(10)	2361571718251217387	0 2 24 26 42 44 60 62 84 86	-2219024729040
SPT(16)	2361572996322398701	0 30 66 72 138 148 156 166 222 232 240 250 316 322 358 388	-940953547726
STPT(10)	2361573024342280739	0 2 12 14 90 92 168 170 180 182	-912933665688
SPT(16)	2361573195481689433	0 18 28 54 90 144 150 180 208 238 244 298 334 360 370 388	-741794256994
SPT(16)	2361573454726540381	0 60 70 132 136 148 210 216 292 298 360 372 376 438 448 508	-482549406046
STPT(12)	2361574964418587171	0 2 36 38 48 50 78 80 90 92 126 128	1027142640744
SPT(16)	2361575352319939489	0 4 132 144 160 180 208 214 258 264 292 312 328 340 468 472	1415043993062
STPT(10)	2361576688991480729	0 2 18 20 30 32 42 44 60 62	2751715534302
SPT(20)	2361577656618356497	0 12 40 60 124 192 220 222 234 252 304 322 334 336 364 432 496 516 544 556	3719342410070
SPT(16)	2361577890095409593	0 18 66 90 138 156 200 210 254 264 308 326 374 398 446 464	3952819463166