Prime p₀= 1312514686270293839 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 10 2 64 2 40 2 28 2 16 2 (?)
a_n: 0 2 90 92 102 104 168 170 210 212 240 242 258 260
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: 260
Found by: stoneageman
db: batch=77, k=14, 88 10 64 40 28 16

SPT(16)	1312512932059391203	0 16 66 78 84 88 114 136 198 220 246 250 256 268 318 334	-1754210902636
SPT(16)	1312513337210454061	0 18 22 30 70 96 100 130 138 168 172 198 238 246 250 268	-1349059839778
TPT(14)	1312513436918678021	0 2 60 62 66 68 96 98 150 152 156 158 186 188	-1249351615818
STPT(10)	1312513789632516431	0 2 36 38 78 80 120 122 156 158	-896637777408
SPT(16)	1312514376427814891	0 2 8 18 30 36 50 90 128 168 182 188 200 210 216 218	-309842478948
TPT(14)	1312514508434972987	0 2 42 44 60 62 144 146 300 302 390 392 420 422	-177835320852
STPT(12)	1312514793514979399	0 2 48 50 78 80 90 92 120 122 168 170	107244685560
TPT(14)	1312515330605039597	0 2 54 56 84 86 180 182 192 194 252 254 282 284	644334745758
STPT(10)	1312515453406413437	0 2 24 26 42 44 60 62 84 86	767136119598
STPT(10)	1312516417650701099	0 2 48 50 90 92 132 134 180 182	1731380407260
SPT(16)	1312516977800828663	0 8 14 66 96 108 134 156 218 240 266 278 308 360 366 374	2291530534824