Prime p₀= 1089215896586599499 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 88 2 76 2 28 2 40 2 58 2 (?)
a_n: 0 2 42 44 132 134 210 212 240 242 282 284 342 344
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: 344
Found by: fake
db: batch=76, k=14, 40 88 76 28 40 58

SPT(16)	1089214678723011817	0 30 36 84 106 144 160 174 196 210 226 264 286 334 340 370	-1217863587682
STPT(10)	1089214681986632021	0 2 6 8 18 20 30 32 36 38	-1214599967478
TPT(14)	1089214949802138389	0 2 60 62 72 74 102 104 150 152 168 170 222 224	-946784461110
STPT(10)	1089215272627718849	0 2 18 20 30 32 42 44 60 62	-623958880650
SPT(16)	1089215698860063611	0 18 26 56 156 180 218 240 308 330 368 392 492 522 530 548	-197726535888
STPT(10)	1089215805721139219	0 2 12 14 30 32 48 50 60 62	-90865460280
STPT(10)	1089216080584696061	0 2 6 8 48 50 90 92 96 98	183998096562
SPT(16)	1089216086319973021	0 42 60 82 138 172 190 222 238 270 288 322 378 400 418 460	189733373522
SPT(16)	1089216236989758029	0 14 60 102 120 122 132 140 144 152 162 164 182 224 270 284	340403158530
SPT(16)	1089216594353438389	0 42 60 88 90 94 112 130 132 150 168 172 174 202 220 262	697766838890
SPT(16)	1089217511123678653	0 28 30 40 54 84 138 148 156 166 220 250 264 274 276 304	1614537079154