Prime p₀= 2157935179709686649 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 148 2 70 2 58 2 34 2 88 2 (?)
a_n: 0 2 30 32 180 182 252 254 312 314 348 350 438 440
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: 440
Found by: Landjunge
db: batch=81, k=14, 28 148 70 58 34 88

SPT(16)	2157933077245192229	0 8 54 78 98 114 134 138 164 168 188 204 224 248 294 302	-2102464494420
STPT(10)	2157933355789207037	0 2 30 32 42 44 54 56 84 86	-1823920479612
SPT(16)	2157933398043220909	0 24 34 40 42 60 88 90 172 174 202 220 222 228 238 262	-1781666465740
SPT(16)	2157933434491493357	0 6 26 62 74 84 86 140 156 210 212 222 234 270 290 296	-1745218193292
SPT(16)	2157934151103131887	0 16 22 36 82 84 154 180 226 252 322 324 370 384 390 406	-1028606554762
SPT(16)	2157934159961846579	0 18 42 48 68 78 140 144 308 312 374 384 404 410 434 452	-1019747840070
SPT(16)	2157935844484121311	0 30 58 96 112 120 130 186 232 288 298 306 322 360 388 418	664774434662
STPT(12)	2157936139237101329	0 2 12 14 72 74 78 80 138 140 150 152	959527414680
STPT(10)	2157936367133156549	0 2 42 44 60 62 78 80 120 122	1187423469900
SPT(16)	2157936905670658877	0 32 84 120 140 174 176 186 230 240 242 276 296 332 384 416	1725960972228
SPT(16)	2157937015242223253	0 8 36 44 56 80 114 126 128 140 174 198 210 218 246 254	1835532536604