Prime p₀= 2565444846846875489 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 22 2 16 2 106 2 40 2 100 2 (?)
a_n: 0 2 18 20 42 44 60 62 168 170 210 212 312 314
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: 314
Found by: JayPi
db: batch=82, k=14, 16 22 16 106 40 100

SPT(16)	2565441840369862379	0 80 84 92 102 104 120 162 230 272 288 290 300 308 312 392	-3006477013110
STPT(10)	2565441976142512067	0 2 30 32 42 44 54 56 84 86	-2870704363422
SPT(16)	2565443420448190279	0 40 64 82 88 112 138 148 204 214 240 264 270 288 312 352	-1426398685210
SPT(16)	2565443777881934809	0 30 48 52 90 100 118 160 210 252 270 280 318 322 340 370	-1068964940680
SPT(16)	2565444062482361737	0 46 76 84 96 102 112 124 132 144 154 160 172 180 210 256	-784364513752
SPT(16)	2565444573405571007	0 44 54 56 86 90 174 182 204 212 296 300 330 332 342 386	-273441304482
SPT(16)	2565445925559073519	0 18 40 48 54 58 72 84 88 100 114 118 124 132 154 172	1078712198030
STPT(10)	2565446209612608209	0 2 18 20 30 32 42 44 60 62	1362765732720
SPT(16)	2565446226484807993	0 40 54 64 70 106 126 130 204 208 228 264 270 280 294 334	1379637932504
SPT(18)	2565446268511268413	0 10 118 168 204 220 250 300 358 390 448 498 528 544 580 630 738 748	1421664392924
STPT(10)	2565446321333573147	0 2 30 32 42 44 54 56 84 86	1474486697658