Prime p₀= 2167584978227716739 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 112 2 88 2 46 2 28 2 40 2 (?)
a_n: 0 2 108 110 222 224 312 314 360 362 390 392 432 434
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: 434
Found by: JonS
db: batch=81, k=14, 106 112 88 46 28 40

SPT(16)	2167583839424451719	0 8 14 20 38 68 78 104 138 164 174 204 222 228 234 242	-1138803265020
STPT(10)	2167583893726353041	0 2 30 32 60 62 90 92 120 122	-1084501363698
STPT(10)	2167583899458111749	0 2 18 20 30 32 42 44 60 62	-1078769604990
STPT(10)	2167584289572153539	0 2 42 44 150 152 258 260 300 302	-688655563200
SPT(16)	2167584448460426063	0 48 50 54 78 84 90 98 180 188 194 200 224 228 230 278	-529767290676
SPT(16)	2167584656622110983	0 10 48 54 66 70 76 78 136 138 144 148 160 166 204 214	-321605605756
SPT(16)	2167585318119235601	0 42 48 90 110 116 126 138 200 212 222 228 248 290 296 338	339891518862
SPT(16)	2167585325566605977	0 6 44 54 60 120 152 174 182 204 236 296 302 312 350 356	347338889238
SPT(16)	2167585326274755733	0 30 76 90 106 108 120 216 310 406 418 420 436 450 496 526	348047038994
STPT(12)	2167585403211678179	0 2 72 74 78 80 162 164 168 170 240 242	424983961440
SPT(16)	2167585469021432743	0 6 34 40 48 78 84 106 138 160 166 196 204 210 238 244	490793716004