Prime p₀= 2533689974726375471 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 118 2 160 2 70 2 154 2 28 2 (?)
a_n: 0 2 66 68 186 188 348 350 420 422 576 578 606 608
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: 608
Found by: Ben
db: batch=82, k=14, 64 118 160 70 154 28

STPT(10)	2533688547427445171	0 2 30 32 78 80 126 128 156 158	-1427298930300
SPT(16)	2533688726625822541	0 12 40 112 118 168 196 202 216 222 250 300 306 378 406 418	-1248100552930
SPT(16)	2533688735343590459	0 12 20 68 104 140 144 152 180 188 192 228 264 312 320 332	-1239382785012
SPT(16)	2533689094032777383	0 20 50 84 108 110 138 150 164 176 204 206 230 264 294 314	-880693598088
SPT(16)	2533689717069525011	0 12 26 50 72 86 110 132 140 162 186 200 222 246 260 272	-257656850460
STPT(10)	2533689811452185117	0 2 30 32 42 44 54 56 84 86	-163274190354
SPT(16)	2533690053124327931	0 18 30 42 92 110 120 138 140 158 168 186 236 248 260 278	78397952460
STPT(10)	2533690813572808649	0 2 48 50 90 92 132 134 180 182	838846433178
STPT(10)	2533690882190226557	0 2 30 32 42 44 54 56 84 86	907463851086
SPT(16)	2533691566410738451	0 18 22 40 60 106 112 160 168 216 222 268 288 306 310 328	1591684362980
STPT(10)	2533692163697296211	0 2 36 38 78 80 120 122 156 158	2188970920740