Prime p₀= 743910736579837397 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 16 2 22 2 28 2 16 2 (?)
a_n: 0 2 30 32 42 44 60 62 84 86 114 116 132 134
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: 134
Found by: Theadalus
db: batch=73, k=14, 28 10 16 22 28 16

SPT(16)	743909627775356123	0 8 20 30 68 104 170 174 224 228 294 330 368 378 390 398	-1108804481274
STPT(10)	743909723435526677	0 2 30 32 42 44 54 56 84 86	-1013144310720
SPT(16)	743909859227770919	0 8 24 48 54 60 68 78 80 90 98 104 110 134 150 158	-877352066478
STPT(10)	743909979967024901	0 2 30 32 60 62 90 92 120 122	-756612812496
STPT(10)	743910098610335549	0 2 12 14 90 92 168 170 180 182	-637969501848
SPT(16)	743910636725738843	0 18 56 110 126 168 176 188 216 228 236 278 294 348 386 404	-99854098554
SPT(16)	743910800367948079	0 34 52 60 72 84 102 154 198 250 268 280 292 300 318 352	63788110682
STPT(10)	743910803483389151	0 2 30 32 78 80 126 128 156 158	66903551754
STPT(10)	743910827505156131	0 2 6 8 18 20 30 32 36 38	90925318734
STPT(10)	743910895479271547	0 2 24 26 42 44 60 62 84 86	158899434150
SPT(16)	743911033325471129	0 18 48 72 152 158 182 188 192 198 222 228 308 332 362 380	296745633732