Prime p₀= 2117859224331315497 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 52 2 4 2 10 2 76 2 40 2 (?)
a_n: 0 2 30 32 84 86 90 92 102 104 180 182 222 224
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=80, k=14, 28 52 4 10 76 40

SPT(16)	2117857473770828633	0 8 26 50 104 116 134 140 174 180 198 210 264 288 306 314	-1750560486864
STPT(12)	2117857619406199169	0 2 42 44 48 50 72 74 78 80 120 122	-1604925116328
TPT(14)	2117857936762539677	0 2 12 14 114 116 144 146 210 212 222 224 312 314	-1287568775820
SPT(16)	2117858634024283457	0 2 6 32 62 74 110 114 182 186 222 234 264 290 294 296	-590307032040
SPT(16)	2117858854187235389	0 24 32 38 62 138 140 150 182 192 194 270 294 300 308 332	-370144080108
SPT(16)	2117859118918679027	0 26 42 80 86 110 140 150 152 162 192 216 222 260 276 302	-105412636470
STPT(10)	2117859252377739107	0 2 30 32 42 44 54 56 84 86	28046423610
TPT(14)	2117859535222114139	0 2 42 44 150 152 162 164 210 212 420 422 432 434	310890798642
STPT(10)	2117859960693761699	0 2 48 50 60 62 72 74 120 122	736362446202
SPT(16)	2117860158394081721	0 8 20 26 32 48 110 126 152 168 230 246 252 258 270 278	934062766224
TPT(14)	2117860599885953057	0 2 90 92 102 104 120 122 174 176 282 284 354 356	1375554637560