Prime p₀= 2170586683189991021 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 124 2 28 2 22 2 16 2 70 2 28 2 (?)
a_n: 0 2 126 128 156 158 180 182 198 200 270 272 300 302
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: Landjunge
db: batch=81, k=14, 124 28 22 16 70 28

SPT(16)	2170585767601147069	0 4 34 42 54 88 144 160 222 238 294 328 340 348 378 382	-915588843952
STPT(10)	2170585902504783809	0 2 12 14 90 92 168 170 180 182	-780685207212
STPT(10)	2170585985639604719	0 2 18 20 30 32 42 44 60 62	-697550386302
SPT(16)	2170586256934448329	0 42 48 54 82 144 174 184 228 238 268 330 358 364 370 412	-426255542692
SPT(16)	2170586523302019793	0 34 40 48 54 76 94 120 124 150 168 190 196 204 210 244	-159887971228
SPT(16)	2170586614021834517	0 14 26 36 42 54 56 66 80 90 92 104 110 120 132 146	-69168156504
SPT(16)	2170587017584932787	0 16 60 70 126 130 144 154 156 166 180 184 240 250 294 310	334394941766
STPT(10)	2170587276024021857	0 2 30 32 72 74 114 116 144 146	592834030836
STPT(10)	2170587378732553601	0 2 6 8 18 20 30 32 36 38	695542562580
STPT(10)	2170587454008091967	0 2 30 32 60 62 90 92 120 122	770818100946
TPT(14)	2170587831647647637	0 2 12 14 24 26 30 32 54 56 84 86 162 164	1148457656616