Prime p₀= 2623736223056256461 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 34 2 28 2 22 2 76 2 (?)
a_n: 0 2 30 32 60 62 96 98 126 128 150 152 228 230
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: 230
Found by: JohnMD
db: batch=82, k=14, 28 28 34 28 22 76

SPT(16)	2623735385088884179	0 12 28 40 78 100 112 148 204 240 252 274 312 324 340 352	-837967372282
STPT(10)	2623735489010300501	0 2 126 128 168 170 210 212 336 338	-734045955960
STPT(10)	2623735701622045247	0 2 12 14 42 44 72 74 84 86	-521434211214
SPT(16)	2623735743717563621	0 2 18 26 42 126 132 158 210 236 242 326 342 350 366 368	-479338692840
SPT(16)	2623735978181025193	0 30 70 120 156 166 180 204 226 250 264 274 310 360 400 430	-244875231268
TPT(14)	2623736115470560661	0 2 30 32 48 50 96 98 180 182 240 242 270 272	-107585695800
SPT(16)	2623736565011978569	0 10 40 70 84 108 132 138 154 160 184 208 222 252 282 292	341955722108
STPT(10)	2623736611648027397	0 2 30 32 42 44 54 56 84 86	388591770936
SPT(16)	2623736748746713727	0 56 92 96 140 144 240 282 374 416 512 516 560 564 600 656	525690457266
SPT(16)	2623736794997352691	0 10 30 42 48 70 88 90 178 180 198 220 226 238 258 268	571941096230
SPT(16)	2623736890099784003	0 6 24 26 56 86 96 140 180 224 234 264 294 296 314 320	667043527542