Prime p₀= 2040656758605751607 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 34 2 82 2 34 2 112 2 16 2 (?)
a_n: 0 2 24 26 60 62 144 146 180 182 294 296 312 314
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: 314
Found by: eclipse99
db: batch=80, k=14, 22 34 82 34 112 16

SPT(16)	2040655953427386107	0 2 50 72 80 86 96 116 120 140 150 156 164 186 234 236	-805178365500
STPT(10)	2040656119904155067	0 2 12 14 42 44 72 74 84 86	-638701596540
STPT(10)	2040656363088328127	0 2 42 44 102 104 162 164 204 206	-395517423480
TPT(14)	2040656421877371941	0 2 30 32 126 128 156 158 186 188 198 200 210 212	-336728379666
STPT(10)	2040656527191996269	0 2 48 50 90 92 132 134 180 182	-231413755338
SPT(16)	2040656681768428487	0 30 74 80 86 92 102 114 122 134 144 150 156 162 206 236	-76837323120
SPT(16)	2040656869618900259	0 44 90 104 114 140 158 174 224 240 258 284 294 308 354 398	111013148652
TPT(14)	2040656885139748619	0 2 18 20 30 32 42 44 78 80 162 164 168 170	126533997012
SPT(16)	2040657257185461641	0 12 122 126 156 216 242 258 290 306 332 392 422 426 536 548	498579710034
STPT(10)	2040657262834970807	0 2 24 26 42 44 60 62 84 86	504229219200
SPT(18)	2040657270637110859	0 4 10 24 30 34 42 48 60 82 94 100 108 112 118 132 138 142	512031359252