Prime p₀= 2355024306857608949 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 64 2 10 2 70 2 136 2 40 2 (?)
a_n: 0 2 12 14 78 80 90 92 162 164 300 302 342 344
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: 344
Found by: Time_Traveler
db: batch=81, k=14, 10 64 10 70 136 40

SPT(16)	2355023289310381447	0 46 64 102 130 132 234 244 312 322 424 426 454 492 510 556	-1017547227502
SPT(16)	2355023496712711259	0 14 50 78 128 162 194 260 282 348 380 414 464 492 528 542	-810144897690
SPT(16)	2355023731217050979	0 8 72 78 150 152 192 198 332 338 378 380 452 458 522 530	-575640557970
TPT(14)	2355024056666898311	0 2 30 32 36 38 60 62 90 92 156 158 210 212	-250190710638
SPT(16)	2355024094577671663	0 66 76 90 136 156 160 168 226 234 238 258 304 318 328 394	-212279937286
SPT(16)	2355024267450556099	0 40 54 88 114 118 138 142 210 214 234 238 264 298 312 352	-39407052850
STPT(10)	2355024309295849559	0 2 18 20 30 32 42 44 60 62	2438240610
SPT(16)	2355024380339329471	0 16 36 42 66 196 226 276 292 342 372 502 526 532 552 568	73481720522
SPT(16)	2355024394626328199	0 78 84 92 102 104 158 192 260 294 348 350 360 368 374 452	87768719250
STPT(10)	2355024412000393751	0 2 36 38 78 80 120 122 156 158	105142784802
SPT(16)	2355024465177331729	0 12 42 64 70 82 150 202 210 262 330 342 348 370 400 412	158319722780