Prime p₀= 2352141347219326361 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 76 2 28 2 178 2 40 2 166 2 (?)
a_n: 0 2 30 32 108 110 138 140 318 320 360 362 528 530
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: 530
Found by: Landjunge
db: batch=81, k=14, 28 76 28 178 40 166

SPT(16)	2352138638432731189	0 10 18 28 30 42 48 72 88 112 118 130 132 142 150 160	-2708786595172
STPT(10)	2352138895351710317	0 2 30 32 72 74 114 116 144 146	-2451867616044
STPT(10)	2352139334793131729	0 2 18 20 30 32 42 44 60 62	-2012426194632
STPT(10)	2352139444209612179	0 2 48 50 90 92 132 134 180 182	-1903009714182
TPT(14)	2352139913765761079	0 2 42 44 72 74 102 104 198 200 210 212 240 242	-1433453565282
SPT(16)	2352140401169979331	0 6 22 28 30 46 60 72 106 118 132 148 150 156 172 178	-946049347030
SPT(16)	2352141761593311691	0 6 48 58 90 136 196 198 238 240 300 346 378 388 430 436	414373985330
STPT(10)	2352141813478845959	0 2 18 20 30 32 42 44 60 62	466259519598
STPT(10)	2352142062159696197	0 2 30 32 42 44 54 56 84 86	714940369836
SPT(16)	2352142069762274269	0 22 60 112 138 204 214 238 264 288 298 364 390 442 480 502	722542947908
SPT(16)	2352142421005246153	0 120 130 154 208 226 250 286 378 414 438 456 510 534 544 664	1073785919792