Prime p₀= 2565311629124852129 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 16 2 10 2 10 2 16 2 (?)
a_n: 0 2 18 20 30 32 42 44 60 62
All 10 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 62
Found by: [SG-2W]Kurzer
db: batch=82, k=10, 2 16 2 10 2

SPT(16)	2565309821249815151	0 26 30 32 56 92 110 120 218 228 246 282 306 308 312 338	-1807875036978
SPT(16)	2565309840212645417	0 14 36 50 66 80 86 134 156 204 210 224 240 254 276 290	-1788912206712
SPT(16)	2565310057226052161	0 56 62 78 86 116 182 188 210 216 282 312 320 336 342 398	-1571898799968
SPT(16)	2565310125604419253	0 4 30 34 64 76 100 118 126 144 168 180 210 214 240 244	-1503520432876
SPT(16)	2565310399806239143	0 4 28 58 60 78 100 130 174 204 226 244 246 276 300 304	-1229318612986
SPT(16)	2565311238157249537	0 4 54 60 76 112 126 130 246 250 264 300 316 322 372 376	-390967602592
STPT(10)	2565311905353749969	0 2 18 20 30 32 42 44 60 62	276228897840
SPT(16)	2565311988615937871	0 18 72 122 146 150 168 170 228 230 248 252 276 326 380 398	359491085742
STPT(10)	2565312046498259171	0 2 36 38 78 80 120 122 156 158	417373407042
STPT(10)	2565312313187531597	0 2 30 32 42 44 54 56 84 86	684062679468
STPT(10)	2565312340396125347	0 2 24 26 42 44 60 62 84 86	711271273218