Prime p₀= 740270182852016807 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 28 2 40 2 46 2 76 2 28 2 (?)
a_n: 0 2 12 14 42 44 84 86 132 134 210 212 240 242
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: 242
Found by: Theadalus
db: batch=73, k=14, 10 28 40 46 76 28

SPT(16)	740269210893996457	0 34 60 72 90 102 130 150 196 216 244 256 274 286 312 346	-971958020350
TPT(16)	740269837148763287	0 2 42 44 60 62 300 302 324 326 354 356 462 464 504 506	-345703253520
SPT(16)	740269909781782763	0 54 60 74 84 116 140 164 210 234 258 290 300 314 320 374	-273070234044
SPT(16)	740270005781209979	0 14 38 54 60 74 80 98 150 168 174 188 194 210 234 248	-177070806828
SPT(16)	740270083857740087	0 32 44 54 66 92 110 114 122 126 144 170 182 192 204 236	-98994276720
STPT(10)	740270166903740927	0 2 24 26 42 44 60 62 84 86	-15948275880
STPT(10)	740270508336586649	0 2 78 80 120 122 162 164 240 242	325484569842
STPT(10)	740270509620248819	0 2 42 44 60 62 78 80 120 122	326768232012
SPT(16)	740270603267307001	0 42 70 88 156 172 178 192 226 240 246 262 330 348 376 418	420415290194
SPT(16)	740270846370379567	0 24 34 90 112 126 130 150 196 216 220 234 256 312 322 346	663518362760
STPT(10)	740270979052239959	0 2 42 44 60 62 78 80 120 122	796200223152