Prime p₀= 1016578846735196231 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 34 2 40 2 10 2 4 2 (?)
a_n: 0 2 60 62 90 92 126 128 168 170 180 182 186 188
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: 188
Found by: stoneageman
db: batch=76, k=14, 58 28 34 40 10 4

STPT(10)	1016577168100399187	0 2 60 62 72 74 84 86 144 146	-1678634797044
STPT(10)	1016577382861726097	0 2 24 26 42 44 60 62 84 86	-1463873470134
SPT(16)	1016577797418685039	0 4 48 70 82 102 108 130 132 154 160 180 192 214 258 262	-1049316511192
SPT(16)	1016578252638641659	0 22 124 154 168 172 204 208 234 238 270 274 288 318 420 442	-594096554572
STPT(10)	1016578331139532331	0 2 30 32 78 80 126 128 156 158	-515595663900
SPT(18)	1016578370736953699	0 8 24 38 50 72 78 90 98 204 212 224 230 252 264 278 294 302	-475998242532
STPT(10)	1016578892552392847	0 2 12 14 42 44 72 74 84 86	45817196616
STPT(10)	1016579000469311297	0 2 12 14 72 74 132 134 144 146	153734115066
SPT(16)	1016579126235497141	0 32 48 108 128 150 168 210 248 290 308 330 350 410 426 458	279500300910
STPT(10)	1016579244171783569	0 2 12 14 90 92 168 170 180 182	397436587338
SPT(16)	1016579664525117949	0 34 42 54 64 100 114 142 180 208 222 258 268 280 288 322	817789921718