Prime p₀= 2581345684093806557 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 58 2 196 2 10 2 28 2 10 2 (?)
a_n: 0 2 42 44 102 104 300 302 312 314 342 344 354 356
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: 356
Found by: JayPi
db: batch=82, k=14, 40 58 196 10 28 10

SPT(16)	2581343547116125783	0 4 34 118 138 148 154 208 210 264 270 280 300 384 414 418	-2136977680774
SPT(16)	2581344567202751927	0 20 24 36 110 174 210 264 302 356 392 456 530 542 546 566	-1116891054630
SPT(16)	2581345105789409221	0 6 28 30 40 42 48 52 96 100 106 108 118 120 142 148	-578304397336
STPT(10)	2581345279639582637	0 2 24 26 42 44 60 62 84 86	-404454223920
STPT(10)	2581345318795810751	0 2 30 32 60 62 90 92 120 122	-365297995806
SPT(16)	2581345571304489623	0 18 60 84 96 104 138 200 204 266 300 308 320 344 386 404	-112789316934
SPT(16)	2581345890101317751	0 126 132 152 192 200 222 252 296 326 348 356 396 416 422 548	206007511194
STPT(10)	2581346393506818407	0 2 30 32 42 44 54 56 84 86	709413011850
STPT(10)	2581346631996403541	0 2 6 8 48 50 90 92 96 98	947902596984
STPT(10)	2581346971074230309	0 2 18 20 30 32 42 44 60 62	1286980423752
SPT(16)	2581347568071788291	0 2 12 96 110 132 146 152 210 216 230 252 266 350 360 362	1883977981734