Prime p₀= 2565692710644828857 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 10 2 124 2 58 2 10 2 40 2 (?)
a_n: 0 2 42 44 54 56 180 182 240 242 252 254 294 296
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: 296
Found by: JayPi
db: batch=82, k=14, 40 10 124 58 10 40

SPT(16)	2565691476922419037	0 34 36 52 114 126 136 150 166 180 190 202 264 280 282 316	-1233722409820
SPT(16)	2565691521990835663	0 10 28 64 78 94 120 130 168 178 204 220 234 270 288 298	-1188653993194
SPT(16)	2565691616306525251	0 6 12 42 70 130 138 142 156 160 168 228 256 286 292 298	-1094338303606
STPT(10)	2565691858264194461	0 2 6 8 48 50 90 92 96 98	-852380634396
STPT(10)	2565691942876797149	0 2 18 20 30 32 42 44 60 62	-767768031708
SPT(16)	2565692100306156083	0 30 78 86 96 126 204 276 278 350 428 458 468 476 524 554	-610338672774
SPT(16)	2565692746502761111	0 10 36 46 48 78 108 112 186 190 220 250 252 262 288 298	35857932254
SPT(16)	2565693051136517347	0 70 82 96 100 106 126 166 180 220 240 246 250 264 276 346	340491688490
STPT(10)	2565693210661485557	0 2 42 44 72 74 102 104 144 146	500016656700
STPT(10)	2565693354356012987	0 2 12 14 42 44 72 74 84 86	643711184130
STPT(10)	2565693472686419531	0 2 30 32 78 80 126 128 156 158	762041590674