Prime p₀= 2864992466683804727 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 58 2 40 2 4 2 70 2 10 2 (?)
a_n: 0 2 72 74 132 134 174 176 180 182 252 254 264 266
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: 266
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 70 58 40 4 70 10

STPT(10)	2864990588424170411	0 2 6 8 18 20 30 32 36 38	-1878259634316
SPT(16)	2864990924336774879	0 2 24 32 44 74 84 128 144 188 198 228 240 248 270 272	-1542347029848
SPT(16)	2864991748324687543	0 18 60 64 130 144 148 184 324 360 364 378 444 448 490 508	-718359117184
STPT(10)	2864991908894510009	0 2 18 20 30 32 42 44 60 62	-557789294718
STPT(10)	2864992243814262929	0 2 12 14 90 92 168 170 180 182	-222869541798
STPT(10)	2864992290773423507	0 2 54 56 72 74 90 92 144 146	-175910381220
SPT(16)	2864992639073815729	0 10 24 48 90 108 124 244 294 414 430 448 490 514 528 538	172390011002
SPT(16)	2864993156639856343	0 28 36 58 66 84 96 124 150 178 190 208 216 238 246 274	689956051616
TPT(14)	2864993280196009139	0 2 90 92 132 134 240 242 282 284 288 290 300 302	813512204412
TPT(14)	2864993340534958427	0 2 42 44 90 92 114 116 132 134 354 356 450 452	873851153700
SPT(16)	2864993575177763011	0 12 42 52 72 78 126 180 208 262 310 316 336 346 376 388	1108493958284