Prime p₀= 4305599024591746961 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 16 2 28 2 46 2 70 2 58 2 (?)
a_n: 0 2 30 32 48 50 78 80 126 128 198 200 258 260
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: 260
Found by: Chooka
db: batch=85, k=14, 28 16 28 46 70 58

SPT(16)	4305598458007380593	0 38 56 126 146 170 198 210 236 248 276 300 320 390 408 446	-566584366368
TPT(14)	4305598510557765329	0 2 42 44 102 104 138 140 192 194 228 230 240 242	-514033981632
STPT(10)	4305598707513300497	0 2 24 26 42 44 60 62 84 86	-317078446464
SPT(13)	4305598725377039509	0 60 102 132 138 150 180 210 222 228 258 300 360	-299214707452
SPT(16)	4305598878502000493	0 24 60 74 126 128 138 170 234 266 276 278 330 344 380 404	-146089746468
STPT(10)	4305598923155922149	0 2 18 20 30 32 42 44 60 62	-101435824812
SPT(16)	4305599221992307091	0 48 62 72 150 156 168 240 248 320 332 338 416 426 440 488	197400560130
SPT(16)	4305599304882710959	0 18 28 42 70 102 130 132 148 150 178 210 238 252 262 280	280290963998
SPT(16)	4305599305403371531	0 6 36 40 100 106 132 142 180 190 216 222 282 286 316 322	280811624570
SPT(16)	4305599337508052539	0 22 82 112 124 160 174 190 222 238 252 288 300 330 390 412	312916305578
SPT(16)	4305599599615041421	0 12 16 30 42 70 72 136 156 220 222 250 262 276 280 292	575023294460