Prime p₀= 2850538388356115291 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 70 2 64 2 88 2 148 2 58 2 (?)
a_n: 0 2 18 20 90 92 156 158 246 248 396 398 456 458
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: 458
Found by: JohnMD
db: batch=82, k=14, 16 70 64 88 148 58

TPT(14)	2850537355026301139	0 2 12 14 168 170 222 224 288 290 342 344 390 392	-1033329814152
SPT(16)	2850537563130331537	0 24 52 60 94 106 136 154 162 180 210 222 256 264 292 316	-825225783754
STPT(10)	2850537783596459651	0 2 30 32 78 80 126 128 156 158	-604759655640
STPT(10)	2850538233138582167	0 2 30 32 42 44 54 56 84 86	-155217533124
SPT(16)	2850538256116816919	0 14 68 78 104 174 218 258 260 300 344 414 440 450 504 518	-132239298372
STPT(10)	2850538380000576821	0 2 6 8 48 50 90 92 96 98	-8355538470
SPT(16)	2850538805530026617	0 12 14 90 96 102 140 144 152 156 194 200 206 282 284 296	417173911326
STPT(10)	2850539020331246999	0 2 18 20 30 32 42 44 60 62	631975131708
STPT(10)	2850539092829443571	0 2 6 8 48 50 90 92 96 98	704473328280
TPT(14)	2850539137308907547	0 2 24 26 60 62 282 284 294 296 390 392 462 464	748952792256
SPT(16)	2850539673500280667	0 76 90 96 100 142 202 280 306 384 444 486 490 496 510 586	1285144165376