Prime p₀= 2735870122466427827 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 40 2 46 2 40 2 46 2 22 2 (?)
a_n: 0 2 60 62 102 104 150 152 192 194 240 242 264 266
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: 266
Found by: [SG-2W]Kurzer
db: batch=82, k=14, 58 40 46 40 46 22

TPT(16)	2735869171985154719	0 2 48 50 120 122 192 194 222 224 252 254 330 332 348 350	-950481273108
SPT(16)	2735869502177524553	0 8 18 54 144 150 158 198 206 246 254 260 350 386 396 404	-620288903274
SPT(16)	2735869713183459733	0 18 24 28 34 40 46 84 100 138 144 150 156 160 166 184	-409282968094
SPT(16)	2735869886108482621	0 10 12 36 46 60 66 102 130 166 172 186 196 220 222 232	-236357945206
SPT(16)	2735869972799540903	0 20 86 96 98 110 128 156 170 198 216 228 230 240 306 326	-149666886924
STPT(10)	2735869977125656757	0 2 12 14 42 44 72 74 84 86	-145340771070
SPT(16)	2735870737405875151	0 18 66 70 76 90 108 112 186 190 208 222 228 232 280 298	614939447324
STPT(10)	2735870778314254211	0 2 36 38 78 80 120 122 156 158	655847826384
STPT(10)	2735870883442525637	0 2 30 32 42 44 54 56 84 86	760976097810
STPT(10)	2735870936223074561	0 2 6 8 18 20 30 32 36 38	813756646734
STPT(10)	2735871097934121281	0 2 36 38 78 80 120 122 156 158	975467693454