Prime p₀= 2157283233515283317 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 64 2 52 2 58 2 106 2 100 2 (?)
a_n: 0 2 54 56 120 122 174 176 234 236 342 344 444 446
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: 446
Found by: Landjunge
db: batch=81, k=14, 52 64 52 58 106 100

SPT(16)	2157281527638223549	0 30 34 40 52 84 90 114 118 142 148 180 192 198 202 232	-1705877059768
STPT(10)	2157281611905797987	0 2 30 32 42 44 54 56 84 86	-1621609485330
TPT(14)	2157281715827461877	0 2 24 26 42 44 132 134 210 212 330 332 420 422	-1517687821440
STPT(10)	2157282219854881289	0 2 18 20 30 32 42 44 60 62	-1013660402028
SPT(16)	2157282741707842019	0 24 38 74 108 134 138 140 162 164 168 194 228 264 278 302	-491807441298
SPT(16)	2157282808723814171	0 30 56 60 78 98 126 138 140 152 180 200 218 222 248 278	-424791469146
SPT(16)	2157283320628969597	0 10 16 22 42 72 100 120 142 162 190 220 240 246 252 262	87113686280
SPT(16)	2157283472727602209	0 18 22 28 58 72 78 90 112 124 130 144 174 180 184 202	239212318892
STPT(10)	2157283545953987081	0 2 36 38 78 80 120 122 156 158	312438703764
SPT(16)	2157283722754985807	0 20 42 86 90 114 126 140 156 170 182 206 210 254 276 296	489239702490
STPT(10)	2157284208721728209	0 2 12 14 30 32 48 50 60 62	975206444892