Prime p₀= 2397304560524088911 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 76 2 40 2 10 2 34 2 88 2 (?)
a_n: 0 2 48 50 126 128 168 170 180 182 216 218 306 308
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: 308
Found by: JonS
db: batch=81, k=14, 46 76 40 10 34 88

TPT(14)	2397302965098959219	0 2 12 14 30 32 78 80 108 110 162 164 168 170	-1595425129692
STPT(10)	2397303034091835011	0 2 6 8 18 20 30 32 36 38	-1526432253900
SPT(16)	2397303551130803633	0 8 44 50 54 80 84 110 138 164 168 194 198 204 240 248	-1009393285278
STPT(10)	2397303591477941747	0 2 42 44 72 74 102 104 144 146	-969046147164
STPT(10)	2397304141826842529	0 2 72 74 180 182 288 290 360 362	-418697246382
STPT(10)	2397304202406509321	0 2 30 32 78 80 126 128 156 158	-358117579590
TPT(14)	2397304582902998729	0 2 132 134 162 164 210 212 288 290 420 422 492 494	22378909818
SPT(16)	2397304604230113211	0 6 40 60 76 88 190 238 258 306 408 420 436 456 490 496	43706024300
SPT(16)	2397304707342097391	0 48 60 72 132 146 158 170 198 210 222 236 296 308 320 368	146818008480
SPT(16)	2397304758591791483	0 26 50 68 110 128 134 156 308 330 336 354 396 414 438 464	198067702572
SPT(16)	2397304959171584419	0 12 18 34 40 42 88 118 144 174 220 222 228 244 250 262	398647495508