Prime p₀= 1040128797654713231 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 142 2 166 2 40 2 124 2 28 2 (?)
a_n: 0 2 36 38 180 182 348 350 390 392 516 518 546 548
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: 548
Found by: [SG-2W]Kurzer
db: batch=76, k=14, 34 142 166 40 124 28

STPT(10)	1040127566747455049	0 2 42 44 90 92 138 140 180 182	-1230907258182
TPT(14)	1040127619454733569	0 2 48 50 102 104 168 170 198 200 222 224 258 260	-1178199979662
SPT(16)	1040128181936250047	0 6 12 60 72 114 144 146 180 182 212 254 266 314 320 326	-615718463184
STPT(10)	1040128203320162681	0 2 6 8 48 50 90 92 96 98	-594334550550
SPT(16)	1040128204419178829	0 30 42 84 104 132 152 164 180 192 212 240 260 302 314 344	-593235534402
STPT(10)	1040128626402006017	0 2 30 32 60 62 90 92 120 122	-171252707214
SPT(16)	1040128960365828331	0 6 52 66 120 160 162 192 220 250 252 292 346 360 406 412	162711115100
STPT(10)	1040128962131598539	0 2 12 14 90 92 168 170 180 182	164476885308
SPT(16)	1040129075128006207	0 4 36 40 54 84 100 106 120 126 142 172 186 190 222 226	277473292976
SPT(13)	1040129208063961079	0 12 30 42 72 78 120 162 168 198 210 228 240	410409247848
SPT(16)	1040129475552035611	0 18 22 42 106 120 172 208 210 246 298 312 376 396 400 418	677897322380