Prime p₀= 813751645523236877 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 10 2 58 2 16 2 88 2 16 2 (?)
a_n: 0 2 72 74 84 86 144 146 162 164 252 254 270 272
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: Theadalus
db: batch=73, k=14, 70 10 58 16 88 16

SPT(16)	813751042832490013	0 10 70 88 94 108 124 160 228 264 280 294 300 318 378 388	-602690746864
STPT(10)	813751056397220477	0 2 30 32 42 44 54 56 84 86	-589126016400
SPT(16)	813751066206839161	0 58 60 90 112 142 148 150 238 240 246 276 298 328 330 388	-579316397716
SPT(16)	813751300246657457	0 54 60 72 86 122 144 146 150 152 174 210 224 236 242 296	-345276579420
TPT(14)	813751371418501259	0 2 42 44 72 74 78 80 120 122 162 164 228 230	-274104735618
STPT(10)	813751509717213437	0 2 30 32 42 44 54 56 84 86	-135806023440
SPT(16)	813752376243930769	0 22 24 28 64 78 94 100 252 258 274 288 324 328 330 352	730720693892
TPT(14)	813752426331320849	0 2 18 20 72 74 102 104 228 230 258 260 270 272	780808083972
SPT(16)	813752429607228169	0 18 22 34 48 84 90 144 178 232 238 274 288 300 304 322	784083991292
STPT(10)	813752458099761107	0 2 30 32 72 74 114 116 144 146	812576524230
SPT(16)	813752936366955737	0 6 32 54 74 110 132 144 182 194 216 252 272 294 320 326	1290843718860