Prime p₀= 2356276416028128029 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 28 2 4 2 130 2 16 2 22 2 (?)
a_n: 0 2 42 44 72 74 78 80 210 212 228 230 252 254
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: 254
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 40 28 4 130 16 22

STPT(10)	2356275068954193977	0 2 72 74 102 104 132 134 204 206	-1347073934052
STPT(10)	2356275352675062389	0 2 18 20 30 32 42 44 60 62	-1063353065640
SPT(16)	2356275866707978619	0 20 48 54 78 104 120 180 182 242 258 284 308 314 342 362	-549320149410
SPT(16)	2356275924054695231	0 26 30 36 50 66 68 122 156 210 212 228 242 248 252 278	-491973432798
SPT(13)	2356276011900240851	0 18 42 72 150 198 210 222 270 348 378 402 420	-404127887178
SPT(16)	2356276123636411261	0 10 22 42 90 112 120 130 150 160 168 190 238 258 270 280	-292391716768
STPT(10)	2356276525186085399	0 2 78 80 120 122 162 164 240 242	109157957370
STPT(10)	2356276707078332417	0 2 30 32 42 44 54 56 84 86	291050204388
STPT(10)	2356277345038544969	0 2 18 20 30 32 42 44 60 62	929010416940
SPT(16)	2356277527574698843	0 10 34 58 66 84 96 108 166 178 190 208 216 240 264 274	1111546570814
SPT(16)	2356277539234932043	0 34 40 48 66 100 150 156 178 184 234 268 286 294 300 334	1123206804014