Prime p₀= 800443284700654451 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 46 2 28 2 22 2 28 2 124 2 (?)
a_n: 0 2 48 50 96 98 126 128 150 152 180 182 306 308
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: 308
Found by: scrap
db: batch=73, k=14, 46 46 28 22 28 124

SPT(16)	800442179555282423	0 24 26 54 56 78 98 126 158 186 206 228 230 258 260 284	-1105145372028
SPT(16)	800442393179558807	0 2 30 42 60 62 86 122 150 186 210 212 230 242 270 272	-891521095644
STPT(10)	800442439012589249	0 2 30 32 60 62 90 92 120 122	-845688065202
STPT(10)	800442456701133677	0 2 30 32 72 74 114 116 144 146	-827999520774
SPT(16)	800442622641206813	0 14 36 50 56 116 120 144 206 230 234 294 300 314 336 350	-662059447638
SPT(16)	800442896157758041	0 16 28 30 60 118 126 130 156 160 168 226 256 258 270 286	-388542896410
STPT(10)	800443457983140029	0 2 42 44 60 62 78 80 120 122	173282485578
STPT(10)	800443827047092409	0 2 18 20 30 32 42 44 60 62	542346437958
STPT(10)	800444311098782759	0 2 48 50 90 92 132 134 180 182	1026398128308
SPT(16)	800444482842673579	0 52 82 88 108 120 130 144 148 162 172 184 204 210 240 292	1198142019128
SPT(16)	800444509931305807	0 22 36 46 64 66 84 112 144 172 190 192 210 220 234 256	1225230651356