Prime p₀= 4044853549602060749 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 136 2 40 2 40 2 64 2 88 2 40 2 (?)
a_n: 0 2 138 140 180 182 222 224 288 290 378 380 420 422
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: 422
Found by: Alnitak2019
db: batch=84, k=14, 136 40 40 64 88 40

TPT(14)	4044852538576188791	0 2 6 8 48 50 60 62 126 128 138 140 156 158	-1011025871958
STPT(10)	4044852596497578989	0 2 12 14 30 32 48 50 60 62	-953104481760
STPT(10)	4044852602588668691	0 2 6 8 18 20 30 32 36 38	-947013392058
STPT(10)	4044852957745909427	0 2 24 26 42 44 60 62 84 86	-591856151322
SPT(16)	4044853216072938991	0 18 30 36 42 52 66 100 108 142 156 166 172 178 190 208	-333529121758
STPT(10)	4044853347088173671	0 2 6 8 18 20 30 32 36 38	-202513887078
SPT(16)	4044853596244472021	0 2 62 66 132 138 140 170 258 288 290 296 362 366 426 428	46642411272
SPT(16)	4044854005514085451	0 6 10 58 88 100 108 160 168 220 228 240 270 318 322 328	455912024702
STPT(10)	4044854401557676697	0 2 42 44 72 74 102 104 144 146	851955615948
SPT(16)	4044854430627039187	0 12 30 60 64 70 100 112 114 126 156 162 166 196 214 226	881024978438
SPT(16)	4044854572267891757	0 44 56 90 92 96 134 176 180 222 260 264 266 300 312 356	1022665831008