Prime p₀= 2796289883774662547 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 22 2 28 2 28 2 136 2 16 2 (?)
a_n: 0 2 30 32 54 56 84 86 114 116 252 254 270 272
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: 272
Found by: JohnMD
db: batch=82, k=14, 28 22 28 28 136 16

TPT(14)	2796288541553630309	0 2 30 32 60 62 90 92 102 104 240 242 258 260	-1342221032238
SPT(16)	2796288861469951849	0 18 42 82 84 94 108 112 210 214 228 238 240 280 304 322	-1022304710698
SPT(16)	2796289333324912177	0 54 126 132 142 172 210 244 252 286 324 354 364 370 442 496	-550449750370
SPT(16)	2796289346248851853	0 46 64 66 70 108 138 144 190 196 226 264 268 270 288 334	-537525810694
STPT(10)	2796289621133043389	0 2 12 14 90 92 168 170 180 182	-262641619158
SPT(16)	2796289686262580227	0 4 10 70 90 114 136 144 166 174 196 220 240 300 306 310	-197512082320
SPT(16)	2796290140039999567	0 12 30 40 46 132 144 156 280 292 304 390 396 406 424 436	256265337020
TPT(14)	2796290250898745309	0 2 78 80 90 92 168 170 198 200 258 260 282 284	367124082762
SPT(16)	2796290443595133427	0 10 34 40 42 154 160 172 174 186 192 304 306 312 336 346	559820470880
SPT(16)	2796290845029045407	0 42 50 72 80 86 96 116 120 140 150 156 164 186 194 236	961254382860
SPT(16)	2796291126755419577	0 6 26 36 56 74 92 116 240 264 282 300 320 330 350 356	1242980757030