Prime p₀= 1519207495323673667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 208 2 76 2 82 2 4 2 (?)
a_n: 0 2 30 32 42 44 252 254 330 332 414 416 420 422
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: 422
Found by: crashtech
db: batch=78, k=14, 28 10 208 76 82 4

SPT(16)	1519206181860036161	0 20 42 50 60 86 98 122 126 150 162 188 198 206 228 248	-1313463637506
SPT(13)	1519206268019991269	0 42 102 180 192 210 222 234 252 264 342 402 444	-1227303682398
SPT(16)	1519206409595277209	0 14 42 72 114 134 144 174 380 410 420 440 482 512 540 554	-1085728396458
STPT(10)	1519206819429770057	0 2 30 32 72 74 114 116 144 146	-675893903610
STPT(10)	1519206861362501321	0 2 6 8 48 50 90 92 96 98	-633961172346
SPT(16)	1519206967878905351	0 50 62 102 120 140 186 198 200 212 258 278 296 336 348 398	-527444768316
STPT(10)	1519207852786971827	0 2 30 32 42 44 54 56 84 86	357463298160
SPT(16)	1519208345008089451	0 28 42 58 72 88 100 156 172 228 240 256 270 286 300 328	849684415784
SPT(16)	1519208402065399363	0 66 84 136 148 160 178 196 198 216 234 246 258 310 328 394	906741725696
SPT(16)	1519208525221840279	0 10 30 58 82 114 154 238 264 348 388 420 444 472 492 502	1029898166612
STPT(10)	1519208637872355509	0 2 48 50 60 62 72 74 120 122	1142548681842