Prime p₀= 3416387895956814731 starts a Symmetric tuple of 14 consecutive primes, which form 7 twin primes (STPT).
d_n: 0 2 34 2 70 2 28 2 28 2 70 2 34 2 (?)
a_n: 0 2 36 38 108 110 138 140 168 170 240 242 276 278
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: 278
Found by: suriv
db: batch=83, k=14, 2 34 2 70 2 28 2

SPT(16)	3416385707862164347	0 4 10 24 52 66 70 100 156 186 190 204 232 246 252 256	-2188094650384
TPT(14)	3416386480063997819	0 2 30 32 78 80 120 122 162 164 198 200 222 224	-1415892816912
SPT(16)	3416386619948908961	0 12 18 36 38 50 116 158 210 252 318 330 332 350 356 368	-1276007905770
SPT(16)	3416386711928918657	0 12 20 66 114 156 212 242 264 294 350 392 440 486 494 506	-1184027896074
SPT(16)	3416386939514126779	0 24 42 64 70 82 84 108 304 328 330 342 348 370 388 412	-956442687952
STPT(10)	3416386977630148787	0 2 42 44 72 74 102 104 144 146	-918326665944
TPT(14)	3416387895956814731	0 2 36 38 108 110 138 140 168 170 240 242 276 278	0
STPT(10)	3416388462137828477	0 2 24 26 42 44 60 62 84 86	566181013746
SPT(16)	3416388468046986871	0 6 82 102 130 132 160 186 202 228 256 258 286 306 382 388	572090172140
SPT(16)	3416388608756688221	0 42 56 62 122 128 132 140 198 206 210 216 276 282 296 338	712799873490
STPT(10)	3416388615599675921	0 2 6 8 18 20 30 32 36 38	719642861190