Prime p₀= 915889576281778337 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 190 2 40 2 16 2 118 2 40 2 (?)
a_n: 0 2 30 32 222 224 264 266 282 284 402 404 444 446
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: 446
Found by: Coleslaw
db: batch=76, k=14, 28 190 40 16 118 40

SPT(16)	915888601797871501	0 28 46 60 72 132 142 172 186 216 226 286 298 312 330 358	-974483906836
SPT(16)	915888719258816503	0 18 30 84 114 154 168 226 258 316 330 370 400 454 466 484	-857022961834
SPT(16)	915888853470699281	0 12 20 42 60 68 90 108 140 158 180 188 206 228 236 248	-722811079056
TPT(14)	915889173344659649	0 2 42 44 78 80 168 170 258 260 282 284 312 314	-402937118688
STPT(10)	915889276381479989	0 2 42 44 120 122 198 200 240 242	-299900298348
STPT(10)	915889342933649471	0 2 30 32 78 80 126 128 156 158	-233348128866
TPT(14)	915889608232870727	0 2 42 44 150 152 222 224 240 242 252 254 264 266	31951092390
SPT(16)	915889689131160677	0 20 42 66 114 206 216 222 224 230 240 332 380 404 426 446	112849382340
STPT(10)	915889780076677529	0 2 12 14 30 32 48 50 60 62	203794899192
STPT(10)	915889798955045729	0 2 12 14 90 92 168 170 180 182	222673267392
TPT(14)	915889881749182001	0 2 30 32 60 62 96 98 138 140 180 182 198 200	305467403664