Prime p₀= 2345024139300980519 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 22 2 88 2 64 2 58 2 10 2 (?)
a_n: 0 2 18 20 42 44 132 134 198 200 258 260 270 272
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: 272
Found by: Landjunge
db: batch=81, k=14, 16 22 88 64 58 10

SPT(16)	2345022136848353903	0 44 48 66 68 90 98 114 230 246 254 276 278 296 300 344	-2002452626616
SPT(16)	2345022215131384379	0 50 54 62 84 128 188 194 198 204 264 308 330 338 342 392	-1924169596140
SPT(16)	2345022928089284903	0 26 36 38 66 80 110 158 186 234 264 278 306 308 318 344	-1211211695616
SPT(16)	2345023177914342691	0 28 36 58 100 106 138 148 168 178 210 216 258 280 288 316	-961386637828
SPT(16)	2345023380458032271	0 18 30 50 60 62 78 92 96 110 126 128 138 158 170 188	-758842948248
SPT(16)	2345023786321111537	0 42 76 102 126 202 222 286 300 364 384 460 484 510 544 586	-352979868982
STPT(10)	2345024571871991921	0 2 6 8 18 20 30 32 36 38	432571011402
STPT(10)	2345024617867971407	0 2 30 32 42 44 54 56 84 86	478566990888
TPT(14)	2345025038438979971	0 2 48 50 60 62 90 92 138 140 228 230 258 260	899137999452
STPT(10)	2345025060197811317	0 2 42 44 72 74 102 104 144 146	920896830798
SPT(16)	2345025423878640491	0 86 128 140 200 258 282 308 330 356 380 438 498 510 552 638	1284577659972