Prime p₀= 4387446820377704537 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 10 2 46 2 10 2 94 2 22 2 (?)
a_n: 0 2 42 44 54 56 102 104 114 116 210 212 234 236
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: 236
Found by: Autofuzzy
db: batch=85, k=14, 40 10 46 10 94 22

SPT(16)	4387444369876745629	0 12 58 70 144 202 270 282 310 322 390 448 522 534 580 592	-2450500958908
STPT(10)	4387445188408477397	0 2 42 44 72 74 102 104 144 146	-1631969227140
STPT(10)	4387445645251864379	0 2 18 20 30 32 42 44 60 62	-1175125840158
SPT(13)	4387445804179866889	0 24 30 42 84 90 132 174 180 222 234 240 264	-1016197837648
SPT(16)	4387446188202992689	0 22 40 54 88 112 238 244 258 264 390 414 448 462 480 502	-632174711848
SPT(16)	4387446637717442069	0 8 78 80 122 138 140 150 170 180 182 198 240 242 312 320	-182660262468
STPT(10)	4387447460751595061	0 2 6 8 48 50 90 92 96 98	640373890524
TPT(14)	4387447771910198297	0 2 24 26 84 86 150 152 162 164 222 224 234 236	951532493760
SPT(16)	4387447798739788823	0 18 20 66 74 78 96 108 176 188 206 210 218 264 266 284	978362084286
SPT(16)	4387448027304710299	0 72 88 112 150 180 208 222 268 282 310 340 378 402 418 490	1206927005762
SPT(16)	4387448178346886089	0 24 48 78 84 90 132 150 292 310 352 358 364 394 418 442	1357969181552