Prime p₀= 2307191381314682591 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 88 2 52 2 106 2 46 2 40 2 (?)
a_n: 0 2 66 68 156 158 210 212 318 320 366 368 408 410
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: 410
Found by: Landjunge
db: batch=81, k=14, 64 88 52 106 46 40

SPT(16)	2307189771275839783	0 36 48 76 78 88 114 120 124 130 156 166 168 196 208 244	-1610038842808
STPT(10)	2307189831473162057	0 2 90 92 102 104 114 116 204 206	-1549841520534
STPT(10)	2307190357190832611	0 2 36 38 78 80 120 122 156 158	-1024123849980
STPT(10)	2307190556335429949	0 2 30 32 60 62 90 92 120 122	-824979252642
SPT(16)	2307190773484126897	0 16 42 64 90 96 132 136 180 184 220 226 252 274 300 316	-607830555694
SPT(16)	2307190809575330213	0 6 8 38 66 78 84 138 176 230 236 248 276 306 308 314	-571739352378
SPT(16)	2307191391061687883	0 18 26 30 48 74 104 128 156 180 210 236 254 258 266 284	9747005292
SPT(16)	2307191415686794079	0 92 108 132 164 174 192 210 212 230 248 258 290 314 330 422	34372111488
SPT(16)	2307191695586911349	0 32 38 42 84 108 128 144 248 264 284 308 350 354 360 392	314272228758
SPT(16)	2307192284267709131	0 2 38 60 102 108 122 146 192 216 230 236 278 300 336 338	902953026540
SPT(16)	2307192369679191409	0 10 18 24 52 60 72 90 112 130 142 150 178 184 192 202	988364508818