Prime p₀= 1078197896170080731 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 58 2 100 2 106 2 58 2 52 2 (?)
a_n: 0 2 6 8 66 68 168 170 276 278 336 338 390 392
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: 392
Found by: stoneageman
db: batch=76, k=14, 4 58 100 106 58 52

SPT(16)	1078196893717313509	0 28 42 60 112 132 174 184 198 208 250 270 322 340 354 382	-1002452767222
STPT(10)	1078196945847453737	0 2 30 32 42 44 54 56 84 86	-950322626994
SPT(16)	1078196998291512917	0 2 56 60 72 86 90 122 174 206 210 224 236 240 294 296	-897878567814
STPT(10)	1078197429616022039	0 2 42 44 60 62 78 80 120 122	-466554058692
TPT(14)	1078197767112892187	0 2 144 146 234 236 570 572 612 614 654 656 684 686	-129057188544
SPT(16)	1078197784165364249	0 2 18 84 90 122 140 164 168 192 210 242 248 314 330 332	-112004716482
TPT(14)	1078198021034051987	0 2 12 14 24 26 54 56 60 62 102 104 114 116	124863971256
SPT(16)	1078198134355163999	0 24 38 78 104 114 140 150 188 198 224 234 260 300 314 338	238185083268
STPT(10)	1078198146241318481	0 2 36 38 78 80 120 122 156 158	250071237750
SPT(16)	1078198250378869429	0 28 40 52 82 84 144 150 232 238 298 300 330 342 354 382	354208788698
SPT(16)	1078198292824629209	0 38 74 78 90 102 120 128 204 212 230 242 254 258 294 332	396654548478