Prime p₀= 1831166251999442471 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 52 2 4 2 28 2 82 2 4 2 (?)
a_n: 0 2 66 68 120 122 126 128 156 158 240 242 246 248
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: 248
Found by: Paul
db: batch=79, k=14, 64 52 4 28 82 4

SPT(16)	1831164860407406401	0 22 28 42 96 108 126 160 168 202 220 232 286 300 306 328	-1391592036070
SPT(16)	1831164961192486811	0 30 38 72 126 156 162 168 170 176 182 212 266 300 308 338	-1290806955660
SPT(16)	1831165011409659269	0 92 110 114 120 122 144 170 192 218 240 242 248 252 270 362	-1240589783202
TPT(14)	1831165092701595461	0 2 30 32 66 68 108 110 126 128 180 182 198 200	-1159297847010
SPT(16)	1831165219209111757	0 34 66 76 82 142 154 184 192 222 234 294 300 310 342 376	-1032790330714
TPT(14)	1831165380774666047	0 2 24 26 42 44 60 62 102 104 114 116 150 152	-871224776424
STPT(10)	1831166414123448497	0 2 30 32 42 44 54 56 84 86	162124006026
SPT(16)	1831167128761253033	0 14 36 44 114 128 144 156 188 200 216 230 300 308 330 344	876761810562
SPT(16)	1831167419322284783	0 6 26 38 90 98 120 150 164 194 216 224 276 288 308 314	1167322842312
STPT(10)	1831167895623163379	0 2 42 44 60 62 78 80 120 122	1643623720908
STPT(10)	1831168812499489157	0 2 30 32 60 62 90 92 120 122	2560500046686