Prime p₀= 2356819615584283271 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 10 2 64 2 28 2 58 2 22 2 (?)
a_n: 0 2 78 80 90 92 156 158 186 188 246 248 270 272
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: Paul
db: batch=81, k=14, 76 10 64 28 58 22

SPT(18)	2356818294135983243	0 54 96 98 104 140 150 168 174 230 236 254 264 300 306 308 350 404	-1321448300028
STPT(10)	2356818351579247649	0 2 42 44 60 62 78 80 120 122	-1264005035622
SPT(16)	2356818514050969187	0 4 16 46 72 102 114 142 174 202 214 244 270 300 312 316	-1101533314084
SPT(16)	2356818995310681229	0 28 48 70 100 130 172 174 238 240 282 312 342 364 384 412	-620273602042
SPT(16)	2356819115100284563	0 36 106 178 186 204 208 214 330 336 340 358 366 438 508 544	-500483998708
STPT(10)	2356819515365333111	0 2 30 32 60 62 90 92 120 122	-100218950160
SPT(16)	2356820038803049529	0 12 50 72 90 110 140 162 182 204 234 254 272 294 332 344	423218766258
TPT(14)	2356821121007790761	0 2 18 20 30 32 60 62 120 122 156 158 198 200	1505423507490
STPT(10)	2356821314497751417	0 2 30 32 42 44 54 56 84 86	1698913468146
SPT(16)	2356821523336019791	0 18 30 58 88 100 108 130 198 220 228 240 270 298 310 328	1907751736520
STPT(10)	2356821790317867557	0 2 24 26 42 44 60 62 84 86	2174733584286