Prime p₀= 728849286523332761 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 4 2 40 2 10 2 58 2 34 2 (?)
a_n: 0 2 90 92 96 98 138 140 150 152 210 212 246 248
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: 248
Found by: Theadalus
db: batch=73, k=14, 88 4 40 10 58 34

STPT(10)	728847614731962137	0 2 24 26 42 44 60 62 84 86	-1671791370624
SPT(16)	728847874158021217	0 34 36 46 70 94 120 124 132 136 162 186 210 220 222 256	-1412365311544
STPT(10)	728848187701422779	0 2 12 14 90 92 168 170 180 182	-1098821909982
STPT(10)	728848277661521117	0 2 60 62 72 74 84 86 144 146	-1008861811644
SPT(16)	728849114840638621	0 16 46 48 60 102 130 142 156 168 196 238 250 252 282 298	-171682694140
STPT(10)	728849142013269227	0 2 30 32 42 44 54 56 84 86	-144510063534
STPT(10)	728849290129772639	0 2 42 44 60 62 78 80 120 122	3606439878
STPT(10)	728849522652841451	0 2 36 38 78 80 120 122 156 158	236129508690
STPT(10)	728849596210212821	0 2 36 38 78 80 120 122 156 158	309686880060
SPT(16)	728849649249600311	0 30 60 68 110 158 168 200 210 242 252 300 342 350 380 410	362726267550
SPT(16)	728850013322433413	0 14 38 56 66 78 80 104 120 144 146 158 168 186 210 224	726799100652