Prime p₀= 2124579191956056131 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 52 2 34 2 28 2 70 2 10 2 (?)
a_n: 0 2 36 38 90 92 126 128 156 158 228 230 240 242
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: 242
Found by: Time_Traveler
db: batch=80, k=14, 34 52 34 28 70 10

SPT(16)	2124577316715289087	0 4 10 40 60 84 124 130 144 150 190 214 234 264 270 274	-1875240767044
STPT(10)	2124577883839659299	0 2 18 20 30 32 42 44 60 62	-1308116396832
TPT(14)	2124578118837994217	0 2 24 26 30 32 180 182 192 194 234 236 360 362	-1073118061914
STPT(10)	2124578423450496197	0 2 30 32 162 164 294 296 324 326	-768505559934
SPT(16)	2124578781767023199	0 38 48 60 80 90 98 102 128 132 140 150 170 182 192 230	-410189032932
STPT(10)	2124578787766767359	0 2 18 20 30 32 42 44 60 62	-404189288772
SPT(16)	2124579307510234933	0 18 30 78 100 114 124 130 138 144 154 168 190 238 250 268	115554178802
TPT(14)	2124579546976238249	0 2 18 20 42 44 60 62 72 74 78 80 228 230	355020182118
SPT(16)	2124579873734885383	0 6 40 70 84 90 166 180 190 204 280 286 300 330 364 370	681778829252
SPT(16)	2124579941962156387	0 22 52 60 112 126 132 144 262 274 280 294 346 354 384 406	750006100256
SPT(16)	2124579970599644269	0 10 34 40 88 130 154 160 222 228 252 294 342 348 372 382	778643588138