Prime p₀= 2412313510509638969 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 40 2 94 2 28 2 58 2 (?)
a_n: 0 2 30 32 60 62 102 104 198 200 228 230 288 290
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: 290
Found by: JayPi
db: batch=82, k=14, 28 28 40 94 28 58

SPT(16)	2412313222305076217	0 12 50 80 92 152 164 180 206 222 234 294 306 336 374 386	-288204562752
STPT(10)	2412313247036506907	0 2 30 32 60 62 90 92 120 122	-263473132062
STPT(10)	2412313248603499781	0 2 78 80 138 140 198 200 276 278	-261906139188
STPT(10)	2412313261653101579	0 2 12 14 90 92 168 170 180 182	-248856537390
SPT(16)	2412313404889037863	0 16 54 66 94 96 108 120 154 166 178 180 208 220 258 274	-105620601106
STPT(10)	2412313423374262907	0 2 42 44 72 74 102 104 144 146	-87135376062
SPT(18)	2412313874849252833	0 28 34 76 84 120 174 198 214 270 286 310 364 400 408 450 456 484	364339613864
STPT(10)	2412313950136194569	0 2 48 50 90 92 132 134 180 182	439626555600
STPT(10)	2412313962037706927	0 2 30 32 72 74 114 116 144 146	451528067958
SPT(16)	2412314086387705261	0 6 58 60 72 82 100 126 142 168 186 196 208 210 262 268	575878066292
TPT(14)	2412314234336436707	0 2 114 116 180 182 210 212 222 224 342 344 354 356	723826797738