Prime p₀= 2321991617644951169 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 52 2 4 2 22 2 16 2 10 2 (?)
a_n: 0 2 108 110 162 164 168 170 192 194 210 212 222 224
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: 224
Found by: Landjunge
db: batch=81, k=14, 106 52 4 22 16 10

SPT(16)	2321989780141913873	0 66 68 78 120 138 164 168 176 180 206 224 266 276 278 344	-1837503037296
STPT(10)	2321989898628080267	0 2 30 32 72 74 114 116 144 146	-1719016870902
TPT(14)	2321990048738667287	0 2 54 56 114 116 120 122 192 194 222 224 324 326	-1568906283882
STPT(10)	2321990142013305497	0 2 30 32 42 44 54 56 84 86	-1475631645672
SPT(16)	2321991195431477069	0 2 48 62 78 162 198 308 324 434 470 554 570 584 630 632	-422213474100
STPT(10)	2321991369857135477	0 2 12 14 72 74 132 134 144 146	-247787815692
SPT(16)	2321992791117239459	0 24 32 48 62 90 104 162 170 228 242 270 284 300 308 332	1173472288290
SPT(16)	2321993342711258641	0 40 46 112 132 172 216 250 252 286 330 370 390 456 462 502	1725066307472
STPT(10)	2321993977286487599	0 2 18 20 30 32 42 44 60 62	2359641536430
TPT(14)	2321994194335490357	0 2 60 62 72 74 90 92 114 116 144 146 210 212	2576690539188
SPT(16)	2321994457396955197	0 6 22 52 70 84 94 124 162 192 202 216 234 264 280 286	2839752004028