Prime p₀= 1038582573409774007 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 16 2 16 2 40 2 136 2 22 2 (?)
a_n: 0 2 24 26 42 44 60 62 102 104 240 242 264 266
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: 266
Found by: Theadalus
db: batch=76, k=14, 22 16 16 40 136 22

SPT(16)	1038581222135531947	0 22 46 64 66 90 94 96 160 162 166 190 192 210 234 256	-1351274242060
STPT(10)	1038581296573047737	0 2 42 44 72 74 102 104 144 146	-1276836726270
STPT(10)	1038581469798877397	0 2 30 32 42 44 54 56 84 86	-1103610896610
STPT(12)	1038581740374210881	0 2 30 32 90 92 198 200 258 260 288 290	-833035563126
SPT(16)	1038582137296302923	0 48 56 84 86 146 156 168 176 188 198 258 260 288 296 344	-436113471084
SPT(16)	1038582242634154747	0 22 64 72 130 144 184 204 250 270 310 324 382 390 432 454	-330775619260
SPT(16)	1038582887862770669	0 42 44 72 102 110 132 194 228 290 312 320 350 378 380 422	314452996662
STPT(10)	1038582949861057127	0 2 90 92 102 104 114 116 204 206	376451283120
STPT(10)	1038583394662858727	0 2 12 14 72 74 132 134 144 146	821253084720
SPT(16)	1038584072108159881	0 30 52 58 66 82 126 162 226 262 306 322 330 336 358 388	1498698385874
SPT(18)	1038584093653209889	0 4 30 48 52 64 78 108 118 144 154 184 198 210 214 232 258 262	1520243435882