Prime p₀= 1127368138575634799 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 10 2 10 2 4 2 10 2 208 2 (?)
a_n: 0 2 18 20 30 32 42 44 48 50 60 62 270 272
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: 272
Found by: crashtech
db: batch=76, k=14, 16 10 10 4 10 208

SPT(16)	1127365405787854781	0 6 30 60 78 86 108 116 132 140 162 170 188 218 242 248	-2732787780018
SPT(16)	1127366022940139131	0 76 88 118 120 136 168 178 210 220 252 268 270 300 312 388	-2115635495668
SPT(16)	1127366438341067803	0 16 28 30 58 64 88 118 126 156 180 186 214 216 228 244	-1700234566996
STPT(10)	1127366438550742301	0 2 6 8 18 20 30 32 36 38	-1700024892498
SPT(16)	1127366505335162669	0 12 44 78 80 108 122 134 168 180 194 222 224 258 290 302	-1633240472130
STPT(10)	1127366843013767957	0 2 12 14 42 44 72 74 84 86	-1295561866842
STPT(10)	1127368159465468379	0 2 18 20 30 32 42 44 60 62	20889833580
STPT(10)	1127368667349634649	0 2 42 44 60 62 78 80 120 122	528773999850
SPT(16)	1127368805805819001	0 10 12 40 46 76 120 126 172 178 222 252 258 286 288 298	667230184202
STPT(10)	1127369114709309971	0 2 36 38 78 80 120 122 156 158	976133675172
SPT(16)	1127369208297636401	0 12 38 56 66 96 108 116 132 140 152 182 192 210 236 248	1069722001602