Prime p₀= 2574629711822485589 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 76 2 88 2 22 2 64 2 28 2 (?)
a_n: 0 2 60 62 138 140 228 230 252 254 318 320 348 350
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: 350
Found by: JayPi
db: batch=82, k=14, 58 76 88 22 64 28

STPT(10)	2574627900946810559	0 2 48 50 90 92 132 134 180 182	-1810875675030
TPT(14)	2574627946682381411	0 2 48 50 258 260 306 308 546 548 570 572 678 680	-1765140104178
STPT(10)	2574628403367166841	0 2 36 38 78 80 120 122 156 158	-1308455318748
SPT(16)	2574629126300623411	0 28 42 78 88 130 148 160 180 192 210 252 262 298 312 340	-585521862178
STPT(10)	2574629231732023979	0 2 42 44 60 62 78 80 120 122	-480090461610
STPT(10)	2574629657339646617	0 2 60 62 72 74 84 86 144 146	-54482838972
STPT(10)	2574629819361613721	0 2 36 38 78 80 120 122 156 158	107539128132
SPT(16)	2574630145633618643	0 18 36 50 74 120 138 140 174 176 194 240 264 278 296 314	433811133054
SPT(16)	2574630326009863439	0 38 50 110 140 180 182 222 248 288 290 330 360 420 432 470	614187377850
STPT(10)	2574630631295624129	0 2 42 44 90 92 138 140 180 182	919473138540
STPT(10)	2574630729508470131	0 2 36 38 78 80 120 122 156 158	1017685984542