Prime p₀= 726236880051841997 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 94 2 28 2 10 2 28 2 58 2 (?)
a_n: 0 2 54 56 150 152 180 182 192 194 222 224 282 284
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: 284
Found by: Theadalus
db: batch=73, k=14, 52 94 28 10 28 58

SPT(16)	726235771512852919	0 28 42 48 118 178 204 220 222 238 264 324 394 400 414 442	-1108538989078
TPT(14)	726235794625874651	0 2 30 32 138 140 156 158 306 308 318 320 360 362	-1085425967346
SPT(16)	726235825297875973	0 6 10 66 78 100 106 124 150 168 174 196 208 264 268 274	-1054753966024
SPT(16)	726235988416013633	0 8 18 20 38 96 108 110 174 176 188 246 264 266 276 284	-891635828364
TPT(14)	726236766324984881	0 2 30 32 66 68 108 110 306 308 330 332 348 350	-113726857116
SPT(16)	726236867379825883	0 48 126 144 148 156 186 196 258 268 298 306 310 328 406 454	-12672016114
SPT(16)	726236939591969957	0 20 26 30 42 50 56 114 152 210 216 224 236 240 246 266	59540127960
SPT(16)	726237125029384453	0 16 30 36 70 108 148 174 220 246 286 324 358 364 378 394	244977542456
SPT(16)	726237180760988843	0 8 14 20 30 48 50 84 170 204 206 224 234 240 246 254	300709146846
SPT(16)	726237197818484633	0 54 114 120 140 156 164 176 228 240 248 264 284 290 350 404	317766642636
SPT(16)	726237656169232279	0 24 30 34 42 78 108 112 150 154 184 220 228 232 238 262	776117390282