Prime p₀= 1124900727363961739 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 34 2 22 2 58 2 106 2 28 2 (?)
a_n: 0 2 42 44 78 80 102 104 162 164 270 272 300 302
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: 302
Found by: Theadalus
db: batch=76, k=14, 40 34 22 58 106 28

STPT(10)	1124898943618156697	0 2 12 14 72 74 132 134 144 146	-1783745805042
SPT(16)	1124899343230854707	0 50 80 90 162 164 180 224 270 314 330 332 404 414 444 494	-1384133107032
STPT(10)	1124899762519653119	0 2 18 20 30 32 42 44 60 62	-964844308620
SPT(16)	1124899868672372159	0 2 12 20 42 44 90 104 120 134 180 182 204 212 222 224	-858691589580
SPT(16)	1124900171902675541	0 2 20 36 62 102 126 156 302 332 356 396 422 438 456 458	-555461286198
SPT(16)	1124900233772027149	0 10 34 40 52 54 90 94 138 142 178 180 192 198 222 232	-493591934590
SPT(16)	1124900746247331619	0 4 12 100 142 144 168 220 342 394 418 420 462 550 558 562	18883369880
STPT(10)	1124900754607084991	0 2 6 8 48 50 90 92 96 98	27243123252
STPT(10)	1124900889634354277	0 2 30 32 42 44 54 56 84 86	162270392538
STPT(10)	1124901368117449589	0 2 18 20 30 32 42 44 60 62	640753487850
SPT(16)	1124901474302145389	0 24 44 62 78 80 90 150 152 212 222 224 240 258 278 302	746938183650