Prime p₀= 3096743234037028799 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 16 2 178 2 106 2 40 2 58 2 (?)
a_n: 0 2 42 44 60 62 240 242 348 350 390 392 450 452
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: 452
Found by: Groo
db: batch=83, k=14, 40 16 178 106 40 58

STPT(10)	3096742070277163037	0 2 30 32 72 74 114 116 144 146	-1163759865762
TPT(14)	3096742265840567129	0 2 30 32 42 44 78 80 90 92 162 164 240 242	-968196461670
TPT(14)	3096742324592038391	0 2 36 38 78 80 90 92 126 128 150 152 168 170	-909444990408
TPT(14)	3096742346194645691	0 2 6 8 90 92 96 98 138 140 180 182 210 212	-887842383108
STPT(10)	3096742836625499639	0 2 42 44 90 92 138 140 180 182	-397411529160
STPT(10)	3096742955446082807	0 2 42 44 72 74 102 104 144 146	-278590945992
STPT(10)	3096743280511122269	0 2 18 20 30 32 42 44 60 62	46474093470
STPT(10)	3096743286406421549	0 2 30 32 120 122 210 212 240 242	52369392750
SPT(16)	3096743434581465931	0 10 16 132 148 150 162 166 192 196 208 210 226 342 348 358	200544437132
SPT(16)	3096744100668895769	0 24 30 54 120 138 164 182 360 378 404 422 488 512 518 542	866631866970
STPT(10)	3096744167049438947	0 2 30 32 42 44 54 56 84 86	933012410148