Prime p₀= 2668520567022427457 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 52 2 16 2 130 2 58 2 (?)
a_n: 0 2 30 32 60 62 114 116 132 134 264 266 324 326
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: 326
Found by: [SG-FC] hl
db: batch=82, k=14, 28 28 52 16 130 58

TPT(14)	2668519556394760349	0 2 72 74 108 110 150 152 162 164 240 242 282 284	-1010627667108
SPT(16)	2668519578966701659	0 30 42 70 82 94 114 124 138 148 168 180 192 220 232 262	-988055725798
STPT(10)	2668519680119252159	0 2 12 14 90 92 168 170 180 182	-886903175298
STPT(10)	2668519980357360707	0 2 84 86 132 134 180 182 264 266	-586665066750
STPT(10)	2668520201776507217	0 2 60 62 72 74 84 86 144 146	-365245920240
SPT(16)	2668520401819139047	0 4 10 94 112 130 174 190 276 292 336 354 372 456 462 466	-165203288410
SPT(16)	2668520582555210837	0 12 60 116 122 150 152 156 236 240 242 270 276 332 380 392	15532783380
TPT(14)	2668520724719544689	0 2 12 14 120 122 192 194 330 332 348 350 432 434	157697117232
TPT(14)	2668520802563279957	0 2 102 104 150 152 192 194 210 212 360 362 402 404	235540852500
SPT(16)	2668520901799909349	0 14 18 42 74 78 180 182 240 242 344 348 380 404 408 422	334777481892
SPT(16)	2668521064577719913	0 8 30 50 56 74 80 108 176 204 210 228 234 254 276 284	497555292456