Prime p₀= 2070545583902389409 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 46 2 40 2 28 2 16 2 22 2 (?)
a_n: 0 2 90 92 138 140 180 182 210 212 228 230 252 254
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: 254
Found by: Cruncher Pete
db: batch=80, k=14, 88 46 40 28 16 22

SPT(16)	2070542337367055281	0 10 36 46 72 78 88 112 186 210 220 226 252 262 288 298	-3246535334128
SPT(16)	2070542365677831593	0 6 8 38 60 74 84 104 120 140 150 164 186 216 218 224	-3218224557816
SPT(16)	2070542734257952589	0 8 32 38 50 78 138 150 152 164 224 252 264 270 294 302	-2849644436820
SPT(16)	2070543232819617029	0 12 38 68 78 102 122 140 162 180 200 224 234 264 290 302	-2351082772380
STPT(10)	2070543770277281441	0 2 6 8 18 20 30 32 36 38	-1813625107968
SPT(20)	2070545473539596983	0 10 18 28 70 88 154 160 178 180 334 336 354 360 426 444 486 496 504 514	-110362792426
TPT(14)	2070545880006140219	0 2 12 14 42 44 132 134 138 140 168 170 258 260	296103750810
SPT(13)	2070545976414416227	0 30 72 84 90 114 132 150 174 180 192 234 264	392512026818
STPT(10)	2070546047245205867	0 2 30 32 42 44 54 56 84 86	463342816458
STPT(10)	2070546254019166739	0 2 12 14 30 32 48 50 60 62	670116777330
STPT(10)	2070546320161068689	0 2 42 44 60 62 78 80 120 122	736258679280