Prime p₀= 2729503447639089827 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 4 2 22 2 88 2 46 2 76 2 (?)
a_n: 0 2 24 26 30 32 54 56 144 146 192 194 270 272
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: JayPi
db: batch=82, k=14, 22 4 22 88 46 76

SPT(16)	2729502649883827819	0 18 28 40 42 154 180 198 364 382 408 520 522 534 544 562	-797755262008
SPT(16)	2729502697465107871	0 28 40 66 88 118 126 160 228 262 270 300 322 348 360 388	-750173981956
SPT(16)	2729502961081020353	0 6 54 56 98 110 116 146 228 258 264 276 318 320 368 374	-486558069474
TPT(14)	2729503019346860717	0 2 114 116 132 134 174 176 252 254 270 272 294 296	-428292229110
SPT(16)	2729503148068370677	0 12 22 42 76 82 100 112 120 132 150 156 190 210 220 232	-299570719150
SPT(16)	2729503304280567149	0 2 18 24 48 60 80 102 110 132 152 164 188 194 210 212	-143358522678
SPT(16)	2729503790840536711	0 36 40 42 72 78 108 138 250 280 310 316 346 348 352 388	343201446884
SPT(16)	2729503859936936317	0 6 16 34 36 70 160 186 214 240 330 364 366 384 394 400	412297846490
SPT(16)	2729504268927354839	0 20 32 48 78 90 92 134 138 180 182 194 224 240 252 272	821288265012
TPT(14)	2729504302563286097	0 2 132 134 192 194 210 212 252 254 264 266 300 302	854924196270
SPT(16)	2729504430959275769	0 2 8 38 50 74 122 158 174 210 258 282 294 324 330 332	983320185942