Prime p₀= 2579422163429872259 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 16 2 40 2 106 2 220 2 16 2 (?)
a_n: 0 2 30 32 48 50 90 92 198 200 420 422 438 440
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: 440
Found by: JayPi
db: batch=82, k=14, 28 16 40 106 220 16

SPT(16)	2579420279305605193	0 16 34 64 78 90 120 124 150 154 184 196 210 240 258 274	-1884124267066
STPT(10)	2579420802257229107	0 2 72 74 102 104 132 134 204 206	-1361172643152
STPT(10)	2579421118164333809	0 2 42 44 60 62 78 80 120 122	-1045265538450
SPT(16)	2579421400757427349	0 30 70 82 100 102 142 198 214 270 310 312 330 342 382 412	-762672444910
SPT(16)	2579421672893867761	0 12 36 42 70 82 120 130 138 148 186 198 226 232 256 268	-490536004498
SPT(16)	2579422152790898539	0 42 54 78 82 88 94 112 120 138 144 150 154 178 190 232	-10638973720
SPT(16)	2579422497246460891	0 22 28 42 60 82 88 172 198 282 288 310 328 342 348 370	333816588632
STPT(10)	2579422550475827657	0 2 12 14 42 44 72 74 84 86	387045955398
SPT(16)	2579422875489328993	0 4 28 46 108 124 126 150 154 178 180 196 258 276 300 304	712059456734
SPT(16)	2579423402449178657	0 42 86 152 164 254 264 302 324 362 372 462 474 540 584 626	1239019306398
TPT(14)	2579424210238099907	0 2 12 14 102 104 132 134 144 146 174 176 180 182	2046808227648