Prime p₀= 2864531560377065771 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 10 2 16 2 16 2 22 2 64 2 (?)
a_n: 0 2 78 80 90 92 108 110 126 128 150 152 216 218
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: 218
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 76 10 16 16 22 64

SPT(16)	2864530395369441647	0 36 44 92 104 170 192 246 260 314 336 402 414 462 470 506	-1165007624124
STPT(10)	2864530712584697867	0 2 60 62 72 74 84 86 144 146	-847792367904
STPT(10)	2864531119107032069	0 2 30 32 60 62 90 92 120 122	-441270033702
SPT(16)	2864531194170431239	0 12 42 88 168 172 220 280 282 342 390 394 474 520 550 562	-366206634532
SPT(16)	2864531305355107363	0 40 54 78 84 108 150 178 180 208 250 274 280 304 318 358	-255021958408
STPT(10)	2864531468503118471	0 2 36 38 78 80 120 122 156 158	-91873947300
SPT(16)	2864531611122073999	0 10 12 28 30 88 130 144 148 162 204 262 264 280 282 292	50745008228
TPT(14)	2864532226770431837	0 2 72 74 90 92 144 146 174 176 180 182 222 224	666393366066
STPT(10)	2864532241083951047	0 2 30 32 42 44 54 56 84 86	680706885276
STPT(10)	2864532943608519707	0 2 30 32 42 44 54 56 84 86	1383231453936
SPT(16)	2864532991476590983	0 48 94 106 108 154 178 238 246 306 330 376 378 390 436 484	1431099525212