Prime p₀= 2040213521209791227 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 40 2 64 2 82 2 4 2 22 2 (?)
a_n: 0 2 42 44 84 86 150 152 234 236 240 242 264 266
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: 266
Found by: Dingo
db: batch=80, k=14, 40 40 64 82 4 22

SPT(16)	2040212594333091209	0 14 42 114 120 140 188 194 198 204 252 272 278 350 378 392	-926876700018
STPT(10)	2040212604436746161	0 2 36 38 78 80 120 122 156 158	-916773045066
STPT(10)	2040212778829045157	0 2 30 32 42 44 54 56 84 86	-742380746070
SPT(16)	2040212891744328473	0 14 30 50 60 74 110 116 198 204 240 254 264 284 300 314	-629465462754
SPT(16)	2040213011991861391	0 16 28 48 60 72 88 132 136 180 196 208 220 240 252 268	-509217929836
STPT(10)	2040213376080932357	0 2 30 32 42 44 54 56 84 86	-145128858870
SPT(16)	2040213667084899409	0 4 22 70 244 250 270 334 468 532 552 558 732 780 798 802	145875108182
STPT(10)	2040214300977829589	0 2 18 20 30 32 42 44 60 62	779768038362
SPT(16)	2040214819254984829	0 78 88 100 130 142 178 190 282 294 330 342 372 384 394 472	1298045193602
STPT(10)	2040214925978213627	0 2 30 32 42 44 54 56 84 86	1404768422400
STPT(10)	2040215056544490071	0 2 36 38 78 80 120 122 156 158	1535334698844