Prime p₀= 2299258315831990391 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 124 2 28 2 112 2 28 2 4 2 28 2 (?)
a_n: 0 2 126 128 156 158 270 272 300 302 306 308 336 338
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: 338
Found by: JonS
db: batch=81, k=14, 124 28 112 28 4 28

SPT(16)	2299257062415300583	0 4 24 58 70 88 148 156 178 186 246 264 276 310 330 334	-1253416689808
STPT(12)	2299257487986743747	0 2 12 14 72 74 150 152 210 212 222 224	-827845246644
STPT(10)	2299257527505021437	0 2 12 14 72 74 132 134 144 146	-788326968954
SPT(16)	2299258279042712101	0 28 70 72 100 108 112 132 298 318 322 330 358 360 402 430	-36789278290
SPT(16)	2299258284949476559	0 10 34 112 118 154 210 238 294 322 378 414 420 498 522 532	-30882513832
TPT(14)	2299258307872092527	0 2 30 32 42 44 132 134 174 176 204 206 240 242	-7959897864
STPT(10)	2299258484129632931	0 2 6 8 48 50 90 92 96 98	168297642540
SPT(16)	2299258730130312283	0 28 34 36 40 46 90 120 124 154 198 204 208 210 216 244	414298321892
SPT(16)	2299258751405006779	0 12 24 34 40 112 120 138 274 292 300 372 378 388 400 412	435573016388
TPT(14)	2299258818817781729	0 2 30 32 150 152 192 194 198 200 240 242 282 284	502985791338
STPT(10)	2299259548958946491	0 2 30 32 78 80 126 128 156 158	1233126956100