Prime p₀= 1115191173571812581 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 124 2 100 2 88 2 76 2 178 2 22 2 (?)
a_n: 0 2 126 128 228 230 318 320 396 398 576 578 600 602
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: 602
Found by: Theadalus
db: batch=76, k=14, 124 100 88 76 178 22

SPT(16)	1115190341114468629	0 10 40 52 54 108 154 190 222 258 304 358 360 372 402 412	-832457343952
TPT(14)	1115190437113590041	0 2 66 68 138 140 198 200 276 278 306 308 318 320	-736458222540
SPT(16)	1115190638144361349	0 18 28 58 130 148 160 174 268 282 294 312 384 414 424 442	-535427451232
SPT(16)	1115190669016830827	0 116 120 152 176 186 200 210 212 222 236 246 270 302 306 422	-504554981754
STPT(10)	1115190711225351989	0 2 42 44 90 92 138 140 180 182	-462346460592
SPT(16)	1115191103922526703	0 8 18 36 74 120 128 176 198 246 254 300 338 356 366 374	-69649285878
SPT(16)	1115191304230902167	0 24 44 62 104 120 150 164 180 194 224 240 282 300 320 344	130659089586
STPT(10)	1115191394004551597	0 2 30 32 42 44 54 56 84 86	220432739016
TPT(14)	1115192221984555751	0 2 156 158 168 170 180 182 240 242 246 248 420 422	1048412743170
STPT(10)	1115192239552489361	0 2 6 8 48 50 90 92 96 98	1065980676780
SPT(16)	1115192339881801351	0 36 46 52 60 66 108 112 126 130 172 178 186 192 202 238	1166309988770