Prime p₀= 1144726469525877671 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 40 2 130 2 28 2 46 2 16 2 (?)
a_n: 0 2 66 68 108 110 240 242 270 272 318 320 336 338
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: 338
Found by: Putin Has a Small Dick
db: batch=76, k=14, 64 40 130 28 46 16

SPT(16)	1144725487140233291	0 2 18 80 90 96 152 156 182 186 242 248 258 320 336 338	-982385644380
SPT(16)	1144725707580607531	0 46 52 58 60 126 142 148 150 156 172 238 240 246 252 298	-761945270140
SPT(16)	1144725992788103599	0 4 102 154 184 198 228 238 324 334 364 378 408 460 558 562	-476737774072
STPT(10)	1144726184857525901	0 2 36 38 78 80 120 122 156 158	-284668351770
STPT(10)	1144726208340095201	0 2 6 8 18 20 30 32 36 38	-261185782470
SPT(18)	1144726280218795871	0 38 72 78 102 200 318 392 408 422 438 512 630 728 752 758 792 830	-189307081800
TPT(14)	1144726553772077201	0 2 6 8 48 50 78 80 90 92 120 122 156 158	84246199530
STPT(10)	1144727175877663529	0 2 48 50 90 92 132 134 180 182	706351785858
SPT(16)	1144727227454607091	0 60 78 88 96 102 120 126 142 148 166 172 180 190 208 268	757928729420
STPT(10)	1144727340170335697	0 2 12 14 42 44 72 74 84 86	870644458026
SPT(16)	1144727656820684549	0 30 32 78 110 120 138 152 228 242 260 270 302 348 350 380	1187294806878